List of the Longest Prime Siteswaps

Below are listed the longest prime siteswaps for a variety of cases, organized by number of balls and maximum throw value. Throws greater than 9 are listed as A, B, C, and so on. For an explanation and summary of these results please refer to the accompanying article.

Calculation times listed below are from a variety of machines and versions of the algorithm. They are for entertainment purposes only.


2 Balls


2 Balls, Height 3

(L, Lbound, States) = (3, 3, 3)

330

2 Balls, Height 4

(L, Lbound, States) = (4, 4, 6)

4130
4400

2 Balls, Height 5

(L, Lbound, States) = (8, 8, 10)

Complete: (1 pattern)
  +2-+-4--

2 Balls, Height 6

(L, Lbound, States) = (12, 12, 15)

Complete: (1 pattern)
  +2-5--+-5---

2 Balls, Height 7

(L, Lbound, States) = (18, 18, 21)

Complete: (1 pattern)
  +3--+--6---+-6----

2 Balls, Height 8

(L, Lbound, States) = (24, 24, 28)

Complete: (1 pattern)
  +3--7---+--7----+-7-----

2 Balls, Height 9

(L, Lbound, States) = (32, 32, 36)

Complete: (1 pattern)
  +4---+---8----+--8-----+-8------

2 Balls, Height 10

(L, Lbound, States) = (40, 40, 45)

Complete: (1 pattern)
  +4---9----+---9-----+--9------+-9-------

2 Balls, Height 11

(L, Lbound, States) = (50, 50, 55)

Complete: (1 pattern)
  +5----+----A-----+---A------+--A-------+-A--------

2 Balls, Height 12

(L, Lbound, States) = (60, 60, 66)

Complete: (1 pattern)
  +5----B-----+----B------+---B-------+--B--------+-B---------

3 Balls


3 Balls, Height 4

(L, Lbound, States) = (4, 4, 4)

  4440

3 Balls, Height 5

(L, Lbound, States) = (8, 8, 10)

Complete: (1 pattern)
  ++1+-+3-

3 Balls, Height 6

(L, Lbound, States) = (15, 16, 20)

Type I Incomplete: (6 patterns)
  ++2-+-+2-++-5--
  ++2-+-+11++-5--
  ++1+--+4-+-+4--  
  ++1+--+4-+-+13-  
  ++1+--55-+-+4--
  +35-+-+2-++-5--
Type II Incomplete: (0 patterns)


3 Balls, Height 7

(L, Lbound, States) = (30, 30, 35)

Complete: (1 pattern)
  ++3--+-+1+--+-6-+--+4--++-6---  

3 Balls, Height 8

(L, Lbound, States) = (49, 49, 56)

Complete: (3 patterns)
  ++2-+---+5--+-+-7---+-+2-+--+-7--+--+5---++-7----
  ++2-+---+6--+--+2-+-+--7--+-+-7---+-+4---++-7----
  ++1+----+6-+---+6--+--+2-+-+--7--+-+-7---+-+6----

3 Balls, Height 9

(L, Lbound, States) = (74, 74, 84)

Complete: (1 pattern)
  ++5----+-+1+----+-8-+----+7--+---+1+--+---8-8--+--+-8---+--+6----++-8-----

3 Balls, Height 10

(L, Lbound, States) = (108, 108, 120)

Complete: (0 patterns)
  ++3--+----+6---+-+--9----+-+-9-----+-+4---+--+-9----+--+2-+---+--9--+---+-9---+---+6----++--9-----++-9------

3 Balls, Height 11

(L, Lbound, States) = (149, 150, 165)

Type I Incomplete: (18 patterns)
  ++7------+-+4---+---+-A----+---+3--+--+---A---+--+--A----+--+-A-----+--+5----+-+--A-----+-+-2-+----+-A---+----+6----++---A-----++--A------++-A-------
  ++6-----+--+2-+----+--A--+----+-A---+----+7----+-+--A-----+-+-A------+-+5----+--+-2-+---+--A---+---+-A----+---+5----++---A-----++--A------++-A-------
  ++5----+---+3--+--+---A---+--+--A----+--+-A-----+--+8------++-1+------+9--+-----+9---+----+3--+-+----A---+-+---A----+-+--A-----+-+-A------+-+9-------
  ++5----+---+3--+--+---A---+--+--A----+--+-A-----+--+6-----++--A------++-2-+-----+9---+----+3--+-+----A---+-+---A----+-+--A-----+-+-A------+-+9-------
  ++4---+----+1+---+----A-+---+---9--+---+-A----+---+8-----+-+-A------+-+2-+-----+-A--+-----+7---+--+--A----+--+-A-----+--+6-----++--A------++-A-------
  ++4---+----+1+---+----9-+---+--A---+---+-A----+---+8-----+-+-A------+-+2-+-----+-A--+-----+7---+--+--A----+--+-A-----+--+6-----++--A------++-A-------
  ++3--+-----+9---+----+9----+---+4---+-+---A----+-+--A-----+-+-A------+-+4---+---+-2-+--+---A---+--+--A----+--+-A-----+--+6-----++--A------++-A-------
  ++3--+-----+9---+----+9----+---+3--+--+---A---+--+--A----+--+-A-----+--+8------++-1+------+5--+-+----A---+-+---A----+-+--A-----+-+-A------+-+9-------
  ++3--+-----+8---+---+-A----+---+3--+--+---A---+--+--A----+--+-A-----+--+8------++-1+------+8--+----+-A---+----+7----+-+--A-----+-+-A------+-+9-------
  ++3--+-----+8---+---+-2-+--+---A---+--+--A----+--+-A-----+--+5----+-+--A-----+-+-A------+-+3--+----+-A---+----+9----+---+7-----++--A------++-A-------
  ++2-+------+9--+-----+9---+----+9----+---+4---+-+---A----+-+--A-----+-+-A------+-+4---+---+-2-+--+---A---+--+--A----+--+-A-----+--+8------++-A-------
  ++2-+------+9--+-----+8---+---+-A----+---+3--+--+---A---+--+--A----+--+-A-----+--+9------+-+3--+----+-A---+----+7----+-+--A-----+-+-6-----++-A-------
  ++2-+------+9--+-----+8---+---+-A----+---+3--+--+---9---+--+-A-----+--+2-+----+--A--+----+-A---+----+7----+-+--A-----+-+-A------+-+7------++-A-------
  ++2-+------+8--+----+-A---+----+9----+---+8-----+-+-A------+-+2-+-----+-A--+-----+8---+---+-2-+--+---A---+--+--A----+--+-A-----+--+8------++-A-------
  ++2-+------+5--+-+----A---+-+---9----+-+-A------+-+2-+-----+-A--+-----+9---+----+9----+---+3--+--+---A---+--+--A----+--+-A-----+--+8------++-A-------
  ++1+-------+9-+------+9--+-----+8---+---+-A----+---+3--+--+---A---+--+--A----+--+-A-----+--+9------+-+3--+----+-A---+----+7----+-+--A-----+-+-8------
  ++1+-------+9-+------+9--+-----+8---+---+-A----+---+3--+--+---9---+--+-A-----+--+2-+----+--A--+----+-A---+----+7----+-+--A-----+-+-A------+-+9-------
  ++1+-------+7-+----+--A--+----+-A---+----+7----+-+--A-----+-+-A------+-+5----+--+-A-----+--+3--+---+--A---+---+-A----+---+5----++---A-----++--9------
Type II Incomplete: (0 patterns)


3 Balls, Height 12

(L, Lbound, States) = (200, 201, 220)

Type I Incomplete: (28 patterns)
  ++8-------+-+3--+-----+-B---+-----+8----+--+--B-----+--+-B------+--+6-----+-+--B------+-+-3--+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+6-----++---B------++--B-------++-B--------
  ++8-------+-+2-+------+-B--+------+9---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+9------+-+-2-+-----+-B---+-----+8----+--+--B-----+--+-B------+--+7------++--B-------++-B--------
  ++4---+-----+8----+--+--B-----+--+-B------+--+9-------++-1+-------+A--+------+9---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+5----+-+---B-----+-+--B------+-+-B-------+-+A--------
  ++4---+-----+8----+--+--B-----+--+-B------+--+7------++--B-------++-2-+------+9---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+5----+-+---B-----+-+--B------+-+-B-------+-+A--------
  ++4---+-----+1+---+-----B-+---+----B--B---+---+--B----+---+-B-----+---+A------+--+5----+--+--B-----+--+-5----+-+--B------+-+-B-------+-+4---+----+-B----+----+7-----++---B------++--B-------++-B--------
  ++4---+-----+1+---+-----A-B---+---+--B----+---+-B-----+---+4---+--+---B----+--+--B-----+--+-B------+--+6-----+-+--B------+-+-B-------+-+4---+----+-B----+----+7-----++---B------++--B-------++-B--------
  ++3--+------+A---+-----+A----+----+4---+-+----B----+-+---B-----+-+--A------+-+1+-------+-B-+-------+7--B---+---+--B----+---+-B-----+---+4---+--+---B----+--+--B-----+--+-B------+--+9-------++-B--------
  ++3--+------+A---+-----+7----+-+---B-----+-+--B------+-+-B-------+-+4---+----+-B----+----+A-----+---+3--B---+---+--B----+---+-3--+--+---B----+--+--B-----+--+-B------+--+7------++--B-------++-B--------
  ++3--+------+A---+-----+7----+-+---B-----+-+--B------+-+-B-------+-+4---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+A------+--+5----+--+--B-----+--+-6-----++--B-------++-B--------
  ++3--+------+9---+----+-B----+----+8-----+-+--B------+-+-B-------+-+6-----+--+-B------+--+2-+-----+--A--+-----+1+---+-----B-+---+----B--B---+---+--B----+---+-B-----+---+8------++--B-------++-B--------
  ++3--+------+9---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+A------+--+6-----+-+--B------+-+-B-------+-+3--+-----+-B---+-----+8----+--+--B-----+--+-6-----++--B-------++-B--------
  ++3--+------+9---+----+-7----+-+--B------+-+-B-------+-+6-----+--+-B------+--+2-+-----+--B--+-----+-B---+-----+A----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+8------++--B-------++-B--------
  ++3--+------+6---+-+----B----+-+---B-----+-+--B------+-+-B-------+-+6-----+--+-B------+--+2-+-----+--A--+-----+A----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+8------++--B-------++-B--------
  ++3--+------+6---+-+----A----+-+--B------+-+-B-------+-+6-----+--+-B------+--+2-+-----+--B--+-----+-B---+-----+A----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+8------++--B-------++-B--------
  ++2-+-------+A--+------+A---+-----+8----+--+--B-----+--+-B------+--+A-------+-+4---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+5----+-+---B-----+-+--B------+-+-7------++-B--------
  ++2-+-------+A--+------+A---+-----+8----+--+--B-----+--+-B------+--+3--+----+--B---+----+-B----+----+A-----+---+3--B---+---+--B----+---+-4---+-+---B-----+-+--B------+-+-B-------+-+8-------++-B--------
  ++2-+-------+A--+------+A---+-----+7----+-+---B-----+-+--B------+-+-B-------+-+4---+----+-B----+----+A-----+---+3--B---+---+--B----+---+-3--+--+---B----+--+--B-----+--+-B------+--+9-------++-B--------
  ++2-+-------+A--+------+A---+-----+7----+-+---B-----+-+--B------+-+-B-------+-+4---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+A------+--+5----+--+--B-----+--+-8------++-B--------
  ++2-+-------+A--+------+9---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+A------+--+6-----+-+--B------+-+-B-------+-+3--+-----+-B---+-----+8----+--+--B-----+--+-8------++-B--------
  ++2-+-------+9--+-----+-B---+-----+8----+--+--B-----+--+-B------+--+A-------+-+2-+------+-B--+------+9---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+9------+-+-7------++-B--------
  ++2-+-------+9--+-----+-B---+-----+8----+--+--B-----+--+-B------+--+6-----+-+--B------+-+-B-------+-+4---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+6-----++---A------++-B--------
  ++2-+-------+9--+-----+-B---+-----+8----+--+--A-----+--+1+------+--B-+------+-B--+------+9---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+9------+-+-B-------+-+8-------++-B--------
  ++2-+-------+7--B---+---+--B----+---+-B-----+---+4---+--+---B----+--+--B-----+--+-B------+--+9-------++-2-+------+A---+-----+A----+----+4---+-+----B----+-+---B-----+-+--B------+-+-B-------+-+A--------
  ++1+--------+A-+-------+A--+------+A---+-----+8----+--+--B-----+--+-B------+--+A-------+-+4---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+5----+-+---B-----+-+--B------+-+-9-------
  ++1+--------+A-+-------+A--+------+A---+-----+8----+--+--B-----+--+-B------+--+3--+----+--B---+----+-B----+----+A-----+---+3--B---+---+--B----+---+-4---+-+---B-----+-+--B------+-+-B-------+-+A--------
  ++1+--------+A-+-------+9--+-----+-B---+-----+8----+--+--B-----+--+-B------+--+A-------+-+2-+------+-B--+------+9---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+9------+-+-9-------
  ++1+--------+A-+-------+9--+-----+-B---+-----+8----+--+--A-----+--+1+------+--B-+------+-B--+------+9---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+9------+-+-B-------+-+A--------
  ++1+--------+9-+------+-B--+------+9---+----+-B----+----+2-+---+----B--B---+---+--B----+---+-B-----+---+9------+-+-B-------+-+3--+-----+-B---+-----+8----+--+--B-----+--+-B------+--+7------++--A-------
Type II Incomplete: (2 patterns)
  ++3--+------+A---+-----+7----+-+---B-----+-+--B------+-+-B-------+-+4---+----+-B----+----+3--+--B----+---+-B-----+---+3--B---B---+--+---B----+--+--B-----+--+-B------+--+7------++--B-------++-B--------
  ++2-+-------+A--+------+A---+-----+7----+-+---B-----+-+--B------+-+-B-------+-+4---+----+-B----+----+3--+--B----+---+-B-----+---+3--B---B---+--+---B----+--+--B-----+--+-B------+--+9-------++-B--------

3 Balls, Height 13

(L, Lbound, States) = (263, 264, 286)

Type I Incomplete: (4 patterns, 45 minutes)
    ++8-------+--+3--+-----+--C---+-----+-C----+-----+9-----+--+--C------+--+-6-----+-+--C-------+-+-C--------+-+3--+------+-C---+------+9----+---+--C-----+---+-C------+---+3--+----+---C---+----+--C----+----+-C-----+----+8------++---C-------++--C--------++-C---------
    ++5----+-----+1+----+-----C-+----+----C--+----+---B---+----+-C-----+----+9------+-+--C-------+-+-C--------+-+3--+------+-C---+------+8----+--+---C-----+--+--C------+--+-C-------+--+5----+---+--C-----+---+-C------+---+7------++---C-------++--C--------++-C---------
    ++5----+-----+1+----+-----B-+----+---C---+----+--C----+----+-C-----+----+9------+-+--C-------+-+-C--------+-+3--+------+-C---+------+8----+--+---C-----+--+--C------+--+-C-------+--+5----+---+--C-----+---+-C------+---+7------++---C-------++--C--------++-C---------
    ++2-+--------+9--+-----+--C---+-----+-C----+-----+9-----+--+--C------+--+-C-------+--+7------+-+--C-------+-+-C--------+-+3--+------+-C---+------+9----+---+--C-----+---+-C------+---+3--+----+---C---+----+--C----+----+-C-----+----+8------++---B-------++-C---------
Type II Incomplete: (4 patterns, 6.6 hours)
    ++3--+-------+B---+------+B----+-----+3--+--+-----C---+--C----+----+-C-----+----+5----+-+----C-----+-+---C------+-+--C-------+-+-C--------+-+6-----+---+-C------+---+3--+----+---C---C----+--+---C-----+--+--C------+--+-C-------+--+8-------++--C--------++-C---------
    ++2-+--------+B--+-------+B---+------+B----+-----+3--+--+-----C---+--C----+----+-C-----+----+5----+-+----C-----+-+---C------+-+--C-------+-+-C--------+-+6-----+---+-C------+---+3--+----+---C---C----+--+---C-----+--+--C------+--+-C-------+--+A--------++-C---------
    ++2-+--------+B--+-------+B---+------+9----+---+--C-----+---+-C------+---+3--+----+---C---+----+--C----+----+-C-----+----+5----+-C----+-----+9-----+--+--C------+--+-C-------+--+3--+-----+--C---C-----+-+---C------+-+--C-------+-+-C--------+-+9--------++-C---------
    ++1+---------+B-+--------+B--+-------+B---+------+9----+---+--C-----+---+-C------+---+3--+----+---C---+----+--C----+----+-C-----+----+5----+-C----+-----+9-----+--+--C------+--+-C-------+--+3--+-----+--C---C-----+-+---C------+-+--C-------+-+-C--------+-+B---------

3 Balls, Height 14

(L, Lbound, States) = (337, 338, 364)

Type I Incomplete: (38 patterns, 2 seconds)

inverses of:

  D313131A111131B131A11111520
  D22231A111112A131A111171130
  D23131A111112C13131A1111330
  C51115111A15111811A11171201
  C3131A11111611A131A11116201
  C23131A11112611B131A1111401
  C22411A11112A115111A1511401
  C2231A111112A131A1111711501
  C3131A111112C13131A11113501
  B3131A11112611B131A11116011
  B2411A11112A115111A15116011
  5911A11117111A1511B01161111
  6B1115111A1511181B011171111
  A41B011117111A15111A1125111
  A2611119129111191B011116111
  92912011B161111911A11116111
  4B131A1111161B0131A11116111
  A26111A01A11111281A11116111
  B315111A112411B141B01111411
  B22611119129111191B01111411
  92911201C1261111911A1111411
  B226111A01A11111281A1111411
  4C13131A11113C0131A11111511
  92911201C125111A11191111511
  B2411A2011B1115111A15111511
  92911120D1225111A1119111131
  C22411A2011B1115111A1511131
  C2231A12011B1131A1111711141
  C3131A11120D113131A11113141
  A61111911A1111611A029111112
  B261111911A111141A029111112
  B25111A1119111151A029111112
  C225111A111911113A029111112
  A411A111141C0315111A1151112
  D22231A12011B1131A111171112
  A31A1111151C03131A111171112
  A31A111113D023131A111171112
  D23131A11120D113131A1111312
Type II Incomplete: (0 patterns, 20 seconds)


3 Balls, Height 15

(L, Lbound, States) = (424, 424, 455)

Complete: (1 pattern, 1 second)

inverse of:

  B411411C1151117111A1D1111115111

3 Balls, Height 16

(L, Lbound, States) = (524, 525, 560)

Type I Incomplete: (20 patterns, 43 seconds)

inverses of:

  D51115111C1151117111C15111C111162011
  6C1115111C1151180111C15111C111161111
  D3131B1111112D16111141C0131B11111411
  D3131B111201E1161111411B131B11111411
  A2A111201E12261111A111C1111A11111511
  B22A111201E1261111A1111B111A11111511
  D3131D120111411D1315111B111A11111511
  D3131D201111411D1315111B111A11111511
  D2231D12011181111B15111B111A11111511
  D2231D20111181111B15111B111A11111511
  A2A111120F122261111A111C1111A1111131
  B22A111120F12261111A1111B111A1111131
  E23131D120111411D1315111B111A1111131
  E23131D201111411D1315111B111A1111131
  E22231D12011181111B15111B111A1111131
  E22231D20111181111B15111B111A1111131
  D2261111A111C1111A1111151B02A1111112
  E22261111A111C1111A111113B02A1111112
  D261111A1111B111A1111151C022A1111112
  E2261111A1111B111A111113C022A1111112
Type II Incomplete: (10 patterns, 7.9 minutes)
  ++1+------------+E-+-----------+E--+----------+E---+---------+E----+--------+B-----+----+---F------+----+--F-------+----+-F--------+----+4---+-----+----F----+-----+---F-----+-----+--F------+-----+-F-------+-----+7------+-F-----+-------+B------+---+---F-------+---+--F--------+---+-F---------+---+4---+------+---F----+------+--F-----+------+-F------+------+B-------+--+---F--------+--+--F---------+--+-F----------+--+4---+-------+--F----F-------+-+----F--------+-+---F---------+-+--F----------+-+-F-----------+-+E------------
  ++2-+-----------+E--+----------+E---+---------+E----+--------+B-----+----+---F------+----+--F-------+----+-F--------+----+4---+-----+----F----+-----+---F-----+-----+--F------+-----+-F-------+-----+7------+-F-----+-------+B------+---+---F-------+---+--F--------+---+-F---------+---+4---+------+---F----+------+--F-----+------+-F------+------+B-------+--+---F--------+--+--F---------+--+-F----------+--+4---+-------+--F----F-------+-+----F--------+-+---F---------+-+--F----------+-+-F-----------+-+C-----------++-F------------
  ++2-+-----------+E--+----------+E---+---------+D----+-------+-F-----+-------+C------+----+--F-------+----+-F--------+----+4---+-----+----F----F-----+---+----F------+---+---F-------+---+--F--------+---+-F---------+---+9--------+-+---F---------+-+--F----------+-+-F-----------+-+4---+--------+-F----+--------+D-----+------+-F------+------+4---+---+------F----+---F-----+-----+--F------+-----+-F-------+-----+6-----+--+-----F------+--+----F-------+--+---F--------+--+--F---------+--+-F----------+--+D-----------++-F------------
  ++2-+-----------+D--+---------+-F---+---------+D----+-------+-F-----+-------+C------+----+--F-------+----+-F--------+----+4---+-----+----F----F-----+---+----F------+---+---F-------+---+--F--------+---+-F---------+---+D----------+-+-F-----------+-+2-+----------+-F--+----------+D---+--------+-F----+--------+D-----+------+-F------+------+4---+---+------F----+---F-----+-----+--F------+-----+-F-------+-----+6-----+--+-----F------+--+----F-------+--+---F--------+--+--F---------+--+-F----------+--+D-----------++-F------------
  ++2-+-----------+E--+----------+E---+---------+E----+--------+B-----+----+---F------+----+--F-------+----+-F--------+----+4---+-----+----F----+-----+---F-----+-----+--F------+-----+-F-------+-----+6-----+--F-----+------+-F------+------+A-------+-+----F--------+-+---F---------+-+--F----------+-+-F-----------+-+5----+-------+-F-----+-------+B------+---+---F-------+---+--F--------+---+-F---------+---+4---+------+---F----F------+--+----F-------+--+---F--------+--+--F---------+--+-F----------+--+D-----------++-F------------
  ++3--+----------+E---+---------+D----+-------+-F-----+-------+C------+----+--F-------+----+-F--------+----+4---+-----+----F----F-----+---+----F------+---+---F-------+---+--F--------+---+-F---------+---+9--------+-+---F---------+-+--F----------+-+-F-----------+-+4---+--------+-F----+--------+D-----+------+-F------+------+4---+---+------F----+---F-----+-----+--F------+-----+-F-------+-----+6-----+--+-----F------+--+----F-------+--+---F--------+--+--F---------+--+-F----------+--+B----------++--F-----------++-F------------
  ++3--+----------+E---+---------+E----+--------+B-----+----+---F------+----+--F-------+----+-F--------+----+4---+-----+----F----+-----+---F-----+-----+--F------+-----+-F-------+-----+6-----+--F-----+------+-F------+------+A-------+-+----F--------+-+---F---------+-+--F----------+-+-F-----------+-+5----+-------+-F-----+-------+B------+---+---F-------+---+--F--------+---+-F---------+---+4---+------+---F----F------+--+----F-------+--+---F--------+--+--F---------+--+-F----------+--+B----------++--F-----------++-F------------
  ++3--+----------+E---+---------+E----+--------+E-----+-------+9------+-+-----F-------+-+----F--------+-+---F---------+-+--F----------+-+-F-----------+-+6-----+------+-F------+------+4---+---+------F----+---F-----+-----+--F------+-----+-F-------+-----+6-----+--+-----F------+--+----F-------+--+---F--------+--+--F---------+--+-F----------+--+7------+----+--F-------+----+-F--------+----+4---+-----+----F----F-----+---+----F------+---+---F-------+---+--F--------+---+-F---------+---+C----------++--F-----------++-F------------
  ++3--+----------+D---+--------+-F----+--------+D-----+------+-F------+------+4---+---+------F----+---F-----+-----+--F------+-----+-F-------+-----+6-----+--+-----F------+--+----F-------+--+---F--------+--+--F---------+--+-F----------+--+A---------+-+--F----------+-+-F-----------+-+3--+---------+-F---+---------+D----+-------+-F-----+-------+C------+----+--F-------+----+-F--------+----+4---+-----+----F----F-----+---+----F------+---+---F-------+---+--F--------+---+-F---------+---+C----------++--F-----------++-F------------
  ++4---+---------+E----+--------+E-----+-------+9------+-+-----F-------+-+----F--------+-+---F---------+-+--F----------+-+-F-----------+-+6-----+------+-F------+------+4---+---+------F----+---F-----+-----+--F------+-----+-F-------+-----+6-----+--+-----F------+--+----F-------+--+---F--------+--+--F---------+--+-F----------+--+7------+----+--F-------+----+-F--------+----+4---+-----+----F----F-----+---+----F------+---+---F-------+---+--F--------+---+-F---------+---+A---------++---F----------++--F-----------++-F------------

3 Balls, Height 17

(L, Lbound, States) = (639, 640, 680)

Type I Incomplete: (34 patterns, 3.5 minutes)

inverses of:

  D411D11111117111D14115111D11411C120115111
  D411611112D1411C111111711D01411C111115111
  D4112C1111117111D14160111D11411C111115111
  D41162011E11411C1111117111C1411C111115111
  D313D01111117111D1312B111111A11C111115111
  D911111112C131C111111711E013131C111115111
  D91120111D1131C1111117111D13131C111115111
  D3131C111111711E0131C1111111291C111115111
  D2312B111111A11C1111181111C13D01111116111
  D241161111C1411C1201191111C11D11111116111
  B411C1111191111C11712011E12411C1111116111
  D411720111D12411C1111191111B11C1111116111
  D231C1111111291C111118111D0131C1111116111
  D241701111C1411C1111191111C112C1111116111
  E31312B111111A11C11111411E1313D0111111411
  E22312B111111A11C1111181111C13D0111111411
  E314115111D11411C12011411E1411D1111111411
  E2241161111C1411C1201191111C11D1111111411
  B411C1111191111C11711201F122411C111111411
  E2411720111D12411C1111191111B11C111111411
  E2231C1111111291C111118111D0131C111111411
  E313131C11111411E191120111D1131C111111411
  E3131C1111111291C1111141F013131C111111411
  E313131C1111141F01911111112C131C111111411
  E314160111D11411C11111411E14112C111111411
  E2241701111C1411C1111191111C112C111111411
  F2222411C1111191111B11C120111D11171111141
  F2222411C111119111C011C1111112C1171111141
  G22222411C1111191111B11C120111D1117111112
  C2411C1111191111B11C111111611E04117111112
  C2411C1111191111B11C11111141F024117111112
  D2411C111111611C0411C1111191111C117111112
  E22411C11111141C0411C1111191111C117111112
  G22222411C111119111C011C1111112C117111112
Type II Incomplete: (4 patterns, 43 minutes)
  ++3--+-----------+F---+----------+F----+---------+E-----+-------+-G------+-------+4---+---G-------+----+--G--------+----+-G---------+----+9--------+-+----G---------+-+---G----------+-+--G-----------+-+-G------------+-+5----+--------+-G-----+--------+E------+------+-G-------+------+6-----+--+------G------+--+-----G-------+--+----G--------+--+---G---------+--+--G----------+--+-G-----------+--+7------+-----+--G-------+-----+-G--------+-----+5----+----+-----G-----+----+----G------G----+---+------G-----+---+-----G------+---+----G-------+---+---G--------+---+--G---------+---+-G----------+---+D-----------++--G------------++-G-------------
  ++3--+-----------+E---+---------+-G----+---------+E-----+-------+-G------+-------+4---+---G-------+----+--G--------+----+-G---------+----+D----------+-+--G-----------+-+-G------------+-+3--+----------+-G---+----------+E----+--------+-G-----+--------+E------+------+-G-------+------+6-----+--+------G------+--+-----G-------+--+----G--------+--+---G---------+--+--G----------+--+-G-----------+--+7------+-----+--G-------+-----+-G--------+-----+5----+----+-----G-----+----+----G------G----+---+------G-----+---+-----G------+---+----G-------+---+---G--------+---+--G---------+---+-G----------+---+D-----------++--G------------++-G-------------
  ++4---+----------+F----+---------+E-----+-------+-G------+-------+4---+---G-------+----+--G--------+----+-G---------+----+9--------+-+----G---------+-+---G----------+-+--G-----------+-+-G------------+-+5----+--------+-G-----+--------+E------+------+-G-------+------+6-----+--+------G------+--+-----G-------+--+----G--------+--+---G---------+--+--G----------+--+-G-----------+--+7------+-----+--G-------+-----+-G--------+-----+5----+----+-----G-----+----+----G------G----+---+------G-----+---+-----G------+---+----G-------+---+---G--------+---+--G---------+---+-G----------+---+B----------++---G-----------++--G------------++-G-------------
  ++4---+----------+E----+--------+-G-----+--------+E------+------+-G-------+------+6-----+--+------G------+--+-----G-------+--+----G--------+--+---G---------+--+--G----------+--+-G-----------+--+7------+-----+--G-------+-----+-G--------+-----+5----+----+-----G-----+----+----G------G----+---+------G-----+---+-----G------+---+----G-------+---+---G--------+---+--G---------+---+-G----------+---+A---------+-+---G----------+-+--G-----------+-+-G------------+-+4---+---------+-G----+---------+E-----+-------+-G------+-------+4---+---G-------+----+--G--------+----+-G---------+----+C----------++---G-----------++--G------------++-G-------------

3 Balls, Height 18

(L, Lbound, States) = (769, 770, 816)

Type I Incomplete: (50 patterns, 20 minutes)

inverses of:

  E3161111A1111C11161111C1711111C11F1111111820111
  E41161111C11161111D16111191111C11F1111111820111
  E2411F1111111291111D1161111C11161111D1611160111
  E231711111C11F11111112A1111C11161111D1611160111
  D261111A1111C1112911111C1711111C11F111111701111
  D411F1111111291111D1161111C11161111D16111801111
  D31711111C11F11111112A1111C11161111D16111801111
  C61111A1111C1112911111C1711111C11F1111119011111
  C6111191111C11711111C1G20111111B11111C111711111
  C6111A01111C11711111C1G111111112A1111C111711111
  5D1161111C11161111D1611119111D011F1111111811111
  4D161111A1111C1116111D01711111C11F1111111811111
  D511161111D16111191111C115111E201G1111111161111
  D411611112D161111A1111C1116111D01G1111111161111
  D41125111E1161111A1111C11701111C1G1111111161111
  D3161111C111B1111112D1611118111C01F111111161111
  D511161111D1611119111E011611112C11F111111161111
  D3161111C111B120111E116111181111B1F111111161111
  D511161111D16111191111C160111E1112F111111161111
  C6111191111D1161111D111720111E15111E11111161111
  D511701111D16111191111D1161111D1112E11111161111
  D411F1111111A111112C161111C1116111E016111171111
  D31711111C112E111111B11111C11701111D16111171111
  E2411F1111111A111112C161111C1116111E01611115111
  E41161111D111611112E15111E111111511E01611115111
  E411611112C11F11111115111E15111511F011611115111
  E41161111D1112E1111115111E151160111E11611115111
  E231711111C112E111111B11111C11701111D1611115111
  E41161111D11162011F115111E1111115111D1611115111
  E511161111D1161111C111E111111920111E12611115111
  F22228111111B1F11111112B111B01111C111B111111511
  F22228111111B1F2011111C11111A1111C111B111111511
  F222611112D111711111C16111D0111E111111A11111511
  F22225111E1111711111C701111C111E111111A11111511
  G222228111111B1F11111112B111B01111C111B11111131
  G222228111111B1F2011111C11111A1111C111B11111131
  G2222611112D111711111C16111D0111E111111A1111131
  G222225111E1111711111C701111C111E111111A1111131
  G22222711111C11F11111112B111B01111C111A11111141
  G22222711111C11F2011111C11111A1111C111A11111141
  G2222611112D11161111D116111D0111E11111191111141
  G222225111E111161111D1701111C111E11111191111141
  H222222711111C11F11111112B111B01111C111A1111112
  H222222711111C11F2011111C11111A1111C111A1111112
  B711111C11F111111181111D061111A1111C111A1111112
  B711111C11F11111116111E0261111A1111C111A1111112
  D5111E1111116111D06111191111D1161111D1117111112
  H22222611112D11161111D116111D0111E1111119111112
  H2222225111E111161111D1701111C111E1111119111112
  D261111511F0511161111D1161111C111E1111119111112
Type II Incomplete: (7 patterns, 4.4 hours)
  ++1+--------------+G-+-------------+G--+------------+G---+-----------+G----+----------+G-----+---------+B------+---H-----+-------+--H------+-------+-H-------+-------+C--------+--+----H---------+--+---H----------+--+--H-----------+--+-H------------+--+5----+--------+--H-----+--------+-H------+--------+D-------+----+---H--------+----+--H---------+----+-H----------+----+4---+-------+----H----H-------+---+----H--------+---+---H---------+---+--H----------+---+-H-----------+---+6-----+------+---H------+------+--H-------+------+-H--------+------+4---+-----+------H----H-----+-----+----H------+-----+---H-------+-----+--H--------+-----+-H---------+-----+9--------+-+-----H---------+-+----H----------+-+---H-----------+-+--H------------+-+-H-------------+-+G--------------
  ++2-+-------------+G--+------------+G---+-----------+G----+----------+G-----+---------+B------+---H-----+-------+--H------+-------+-H-------+-------+C--------+--+----H---------+--+---H----------+--+--H-----------+--+-H------------+--+5----+--------+--H-----+--------+-H------+--------+D-------+----+---H--------+----+--H---------+----+-H----------+----+4---+-------+----H----H-------+---+----H--------+---+---H---------+---+--H----------+---+-H-----------+---+6-----+------+---H------+------+--H-------+------+-H--------+------+4---+-----+------H----H-----+-----+----H------+-----+---H-------+-----+--H--------+-----+-H---------+-----+9--------+-+-----H---------+-+----H----------+-+---H-----------+-+--H------------+-+-H-------------+-+E-------------++-H--------------
  ++2-+-------------+G--+------------+G---+-----------+G----+----------+G-----+---------+B------+---H-----+-------+--H------+-------+-H-------+-------+B--------+-+-----H---------+-+----H----------+-+---H-----------+-+--H------------+-+-H-------------+-+6-----+--------+-H------+--------+D-------+----+---H--------+----+--H---------+----+-H----------+----+4---+-------+----H----H-------+---+----H--------+---+---H---------+---+--H----------+---+-H-----------+---+6-----+------+---H------+------+--H-------+------+-H--------+------+4---+-----+------H----H-----+-----+----H------+-----+---H-------+-----+--H--------+-----+-H---------+-----+8-------+--+-----H--------+--+----H---------+--+---H----------+--+--H-----------+--+-H------------+--+F-------------++-H--------------
  ++3--+------------+G---+-----------+G----+----------+G-----+---------+B------+---H-----+-------+--H------+-------+-H-------+-------+B--------+-+-----H---------+-+----H----------+-+---H-----------+-+--H------------+-+-H-------------+-+6-----+--------+-H------+--------+D-------+----+---H--------+----+--H---------+----+-H----------+----+4---+-------+----H----H-------+---+----H--------+---+---H---------+---+--H----------+---+-H-----------+---+6-----+------+---H------+------+--H-------+------+-H--------+------+4---+-----+------H----H-----+-----+----H------+-----+---H-------+-----+--H--------+-----+-H---------+-----+8-------+--+-----H--------+--+----H---------+--+---H----------+--+--H-----------+--+-H------------+--+D------------++--H-------------++-H--------------
  ++3--+------------+G---+-----------+F----+---------+-H-----+---------+E------+------+--H-------+------+-H--------+------+4---+-----+------H----H-----+-----+----H------+-----+---H-------+-----+--H--------+-----+-H---------+-----+D----------+-+---H-----------+-+--H------------+-+-H-------------+-+4---+----------+-H----+----------+A-----+---+------H------+---H-----+-------+--H------+-------+-H-------+-------+C--------+--+----H---------+--+---H----------+--+--H-----------+--+-H------------+--+5----+--------+--H-----+--------+-H------+--------+D-------+----+---H--------+----+--H---------+----+-H----------+----+4---+-------+----H----H-------+---+----H--------+---+---H---------+---+--H----------+---+-H-----------+---+E------------++--H-------------++-H--------------
  ++4---+-----------+F----+---------+-H-----+---------+E------+------+--H-------+------+-H--------+------+4---+-----+------H----H-----+-----+----H------+-----+---H-------+-----+--H--------+-----+-H---------+-----+D----------+-+---H-----------+-+--H------------+-+-H-------------+-+4---+----------+-H----+----------+A-----+---+------H------+---H-----+-------+--H------+-------+-H-------+-------+C--------+--+----H---------+--+---H----------+--+--H-----------+--+-H------------+--+5----+--------+--H-----+--------+-H------+--------+D-------+----+---H--------+----+--H---------+----+-H----------+----+4---+-------+----H----H-------+---+----H--------+---+---H---------+---+--H----------+---+-H-----------+---+C-----------++---H------------++--H-------------++-H--------------
  ++5----+----------+E-----+-------+--H------+-------+-H-------+-------+B--------+-H-----+---------+C------+----+----H-------+----+---H--------+----+--H---------+----+-H----------+----+8-------+---+----H--------+---+---H---------+---+--H----------+---+-H-----------+---+6-----+------+---H------+------+--H-------+------+-H--------+------+D---------+--+---H----------+--+--H-----------+--+-H------------+--+4---+---------+--H----H---------+-+----H----------+-+---H-----------+-+--H------------+-+-H-------------+-+6-----+--------+-H------+--------+2-+-----+--------H--+-----+-------H---+-----+------H----H-----+-----+----H------+-----+---H-------+-----+--H--------+-----+-H---------+-----+C----------++----H-----------++---H------------++--H-------------++-H--------------

3 Balls, Height 19

(L, Lbound, States) = (917, 918, 969)

Type I Incomplete: (0 patterns)

Type II Incomplete: (4 patterns, 21 hours)

++3--+-------------+H---+------------+H----+-----------+G-----+---------+-I------+---------+G-------+-------+-I--------+-------+7------+--+-------I-------+--+------I--------+--+-----I---------+--+----I----------+--+---I-----------+--+--I------------+--+-I-------------+--+8-------+------+--I--------+------+-I---------+------+6-----+----+------I------+----+-----I-------+----+----I--------+----+---I---------+----+--I----------+----+-I-----------+----+B----------+-+----I-----------+-+---I------------+-+--I-------------+-+-I--------------+-+5----+----------+-I-----+----------+G------+--------+-I-------+--------+5----+---I--------+-----+--I---------+-----+-I----------+-----+6-----+-----+-----I------+-----+----I-------I-----+---+-------I------+---+------I-------+---+-----I--------+---+----I---------+---+---I----------+---+--I-----------+---+-I------------+---+F-------------++--I--------------++-I---------------
++3--+-------------+G---+-----------+-I----+-----------+G-----+---------+-I------+---------+G-------+-------+-I--------+-------+7------+--+-------I-------+--+------I--------+--+-----I---------+--+----I----------+--+---I-----------+--+--I------------+--+-I-------------+--+8-------+------+--I--------+------+-I---------+------+6-----+----+------I------+----+-----I-------+----+----I--------+----+---I---------+----+--I----------+----+-I-----------+----+F------------+-+--I-------------+-+-I--------------+-+3--+------------+-I---+------------+G----+----------+-I-----+----------+G------+--------+-I-------+--------+5----+---I--------+-----+--I---------+-----+-I----------+-----+6-----+-----+-----I------+-----+----I-------I-----+---+-------I------+---+------I-------+---+-----I--------+---+----I---------+---+---I----------+---+--I-----------+---+-I------------+---+F-------------++--I--------------++-I---------------
++4---+------------+H----+-----------+G-----+---------+-I------+---------+G-------+-------+-I--------+-------+7------+--+-------I-------+--+------I--------+--+-----I---------+--+----I----------+--+---I-----------+--+--I------------+--+-I-------------+--+8-------+------+--I--------+------+-I---------+------+6-----+----+------I------+----+-----I-------+----+----I--------+----+---I---------+----+--I----------+----+-I-----------+----+B----------+-+----I-----------+-+---I------------+-+--I-------------+-+-I--------------+-+5----+----------+-I-----+----------+G------+--------+-I-------+--------+5----+---I--------+-----+--I---------+-----+-I----------+-----+6-----+-----+-----I------+-----+----I-------I-----+---+-------I------+---+------I-------+---+-----I--------+---+----I---------+---+---I----------+---+--I-----------+---+-I------------+---+D------------++---I-------------++--I--------------++-I---------------
++4---+------------+G----+----------+-I-----+----------+G------+--------+-I-------+--------+5----+---I--------+-----+--I---------+-----+-I----------+-----+6-----+-----+-----I------+-----+----I-------I-----+---+-------I------+---+------I-------+---+-----I--------+---+----I---------+---+---I----------+---+--I-----------+---+-I------------+---+C-----------+-+---I------------+-+--I-------------+-+-I--------------+-+4---+-----------+-I----+-----------+G-----+---------+-I------+---------+G-------+-------+-I--------+-------+7------+--+-------I-------+--+------I--------+--+-----I---------+--+----I----------+--+---I-----------+--+--I------------+--+-I-------------+--+8-------+------+--I--------+------+-I---------+------+6-----+----+------I------+----+-----I-------+----+----I--------+----+---I---------+----+--I----------+----+-I-----------+----+E------------++---I-------------++--I--------------++-I---------------

3 Balls, Height 20

(L, Lbound, States) = (1082, 1083, 1140)

Type I Incomplete: (92 patterns)

inverses of:

  I23131411E1111111411H131411E111111112E11411E111111A1111401
  I22231411E111111181111F1411E111111112E11411E111111A1111401
  H3131411E1111111411H131411E111111112E11411E111111A11116011
  H2231411E111111181111F1411E111111112E11411E111111A11116011
  G31411E111111117111G1411411E111111291111F11411E11111160111
  F411711111E111F1111111181111F1511161111F115111E12011161111
  F411711111E1117111112F15111E11111118111F015111E11111161111
  F411711111E1112E111111181111F1511701111F115111E11111161111
  F411711111E111720111G115111E111111181111E15111E11111161111
  F3131D111111112D131E11111118111G0191111111C111E11111161111
  F3131D12011111E1131E111111181111F191111111C111E11111161111
  F9111111181111E131D11120111G113131D1111111C111E11111161111
  F911111118111F0131D111111112F13131D1111111C111E11111161111
  F3141F0111111181111F1318111111D112D1111111C111E11111161111
  F9111111181111F1411E111111112F114116111F011411E11111161111
  F9111111181111F1411E11120111G11141161111E11411E11111161111
  F31411E111111181111F131811111E011E111111112B11E11111161111
  F2318111111D112D1111111C111E111111911111E141F0111111171111
  F25111711111E15111E120111A11111E11711111E111F1111111171111
  D5111E111111A11111E11711111E1118120111G125111E111111171111
  F51118201111F125111E111111A11111E11711111D111E111111171111
  F231811111E011E111111112B11E111111911111E1411E111111171111
  F291111111C111E111111911111E131D12011111E1131E111111171111
  F291111111C111E11111191111F0131D111111112D131E111111171111
  F25118011111E15111E111111A11111E11711111E1112E111111171111
  G31318111111D112D1111111C111E1111115111G13141F011111115111
  G22318111111D112D1111111C111E111111911111E141F011111115111
  G31511161111F115111E1201115111G1411711111E111F111111115111
  G225111711111E15111E120111A11111E11711111E111F111111115111
  G313131D1111111C111E1111115111E131D11112011H11911111115111
  G31411E111111112F114116111F011411E1111115111G1911111115111
  G31411E11120111G11141161111E11411E1111115111G1911111115111
  G313131D1111111C111E111111511F0131D111111112G1911111115111
  D5111E111111A11111E11711111E1118112011H1225111E11111115111
  G251118201111F125111E111111A11111E11711111D111E11111115111
  G3131811111E011E111111112B11E1111115111G131411E11111115111
  G2231811111E011E111111112B11E111111911111E1411E11111115111
  G31411E11111111711H01411411E111111A111112E1411E11111115111
  G3191111111C111E1111115111G13131D12011111E1131E11111115111
  G2291111111C111E111111911111E131D12011111E1131E11111115111
  G2291111111C111E11111191111F0131D111111112D131E11111115111
  G3191111111C111E111111511H013131D111111112D131E11111115111
  G31511701111F115111E1111115111G1411711111E1112E11111115111
  G225118011111E15111E111111A11111E11711111E1112E11111115111
  G2411411E111111A111112E1411E11111118111G01411E111111116111
  G411411E1111111911112G1411411E111111511G01411E111111116111
  G2411411E111111291111F11411E111111901111F1411E111111116111
  G411411E111111192011H11411411E1111115111F1411E111111116111
  G411411E111111191111E11411E111111920111G12411E111111116111
  G23131D111111112F1711111E11111D1111118111E0131D11111116111
  G318111111D1111E1111115111G13131D12011111E1131D11111116111
  G228111111D1111E111111911111E131D12011111E1131D11111116111
  G23131D11120111G11711111E11111D11111181111D131D11111116111
  G228111111D1111E11111191111F0131D111111112D131D11111116111
  G318111111D1111E111111511H013131D111111112D131D11111116111
  H22411411E111111A111112E1411E11111118111G01411E11111111411
  H2411411E1111111911112G1411411E111111511G01411E11111111411
  H31411411E111111A111112E1411E111111141I0131411E11111111411
  H31411411E111111291111F11411E1111115011H131411E11111111411
  H22411411E111111291111F11411E111111901111F1411E11111111411
  H2411411E111111192011H11411411E1111115111F1411E11111111411
  H2411411E111111191111E11411E111111920111G12411E11111111411
  H223131D111111112F1711111E11111D1111118111E0131D1111111411
  H313131D111111112H131711111E11111D11111141E0131D1111111411
  H2318111111D1111E1111115111G13131D12011111E1131D1111111411
  H2228111111D1111E111111911111E131D12011111E1131D1111111411
  H223131D11120111G11711111E11111D11111181111D131D1111111411
  H313131D11111201I1131711111E11111D111111411D131D1111111411
  H2228111111D1111E11111191111F0131D111111112D131D1111111411
  H2318111111D1111E111111511H013131D111111112D131D1111111411
  H22225111E111111B11111D111E1201111F11118111111D18111111511
  H22225111E111111B1111E0111E11111112E1118111111D18111111511
  H3131411E1111111411H131411E11201111F111411E111111A11111511
  H2231411E111111181111F1411E11201111F111411E111111A11111511
  I222225111E111111B11111D111E1201111F11118111111D1811111131
  I222225111E111111B1111E0111E11111112E1118111111D1811111131
  I23131411E1111111411H131411E11201111F111411E111111A1111131
  I22231411E111111181111F1411E11201111F111411E111111A1111131
  I222225111E111111A11111E11711111D111E1201111F1111811111141
  I222225111E111111A11111E1171111E0111E11111112E111811111141
  I2222411E111111112F11411E11111119111F011411E11111191111141
  I2222411E11120111G111411E111111191111E11411E11111191111141
  J2222225111E111111A11111E11711111D111E1201111F111181111112
  E25111E111111A11111E11711111D111E11111117111G0511181111112
  E25111E111111A11111E11711111D111E1111111511H02511181111112
  F25111E11111117111E05111E111111A11111E11711111E11181111112
  G225111E1111111511E05111E111111A11111E11711111E11181111112
  J2222225111E111111A11111E1171111E0111E11111112E11181111112
  J22222411E111111112F11411E11111119111F011411E1111119111112
  J22222411E11120111G111411E111111191111E11411E1111119111112
  F2411E11111111611H0411411E111111191111E11411E1111119111112
  F2411E1111111141I02411411E111111191111E11411E1111119111112
Type II Incomplete: (4 patterns, 4.3 days)

  ++4---+-------------+I----+------------+I-----+-----------+H------+---------+-J-------+---------+C--------+--+------J---------+--+-----J----------+--+----J-----------+--+---J------------+--+--J-------------+--+-J--------------+--+7------+--------+--J-------+--------+-J--------+--------+5----+----J--------+-----+---J---------+-----+--J----------+-----+-J-----------+-----+B----------+-+-----J-----------+-+----J------------+-+---J-------------+-+--J--------------+-+-J---------------+-+6-----+----------+-J------+----------+G-------+-------+--J--------+-------+-J---------+-------+7------+---+-------J-------+---+------J--------+---+-----J---------+---+----J----------+---+---J-----------+---+--J------------+---+-J-------------+---+8-------+------+---J--------+------+--J---------+------+-J----------+------+6-----+-----+------J------+-----+-----J-------J-----+----+-------J------+----+------J-------+----+-----J--------+----+----J---------+----+---J----------+----+--J-----------+----+-J------------+----+F-------------++---J--------------++--J---------------++-J----------------
  ++4---+-------------+H----+-----------+-J-----+-----------+H------+---------+-J-------+---------+C--------+--+------J---------+--+-----J----------+--+----J-----------+--+---J------------+--+--J-------------+--+-J--------------+--+7------+--------+--J-------+--------+-J--------+--------+5----+----J--------+-----+---J---------+-----+--J----------+-----+-J-----------+-----+F------------+-+---J-------------+-+--J--------------+-+-J---------------+-+4---+------------+-J----+------------+H-----+----------+-J------+----------+G-------+-------+--J--------+-------+-J---------+-------+7------+---+-------J-------+---+------J--------+---+-----J---------+---+----J----------+---+---J-----------+---+--J------------+---+-J-------------+---+8-------+------+---J--------+------+--J---------+------+-J----------+------+6-----+-----+------J------+-----+-----J-------J-----+----+-------J------+----+------J-------+----+-----J--------+----+----J---------+----+---J----------+----+--J-----------+----+-J------------+----+F-------------++---J--------------++--J---------------++-J----------------
  ++5----+------------+I-----+-----------+H------+---------+-J-------+---------+C--------+--+------J---------+--+-----J----------+--+----J-----------+--+---J------------+--+--J-------------+--+-J--------------+--+7------+--------+--J-------+--------+-J--------+--------+5----+----J--------+-----+---J---------+-----+--J----------+-----+-J-----------+-----+B----------+-+-----J-----------+-+----J------------+-+---J-------------+-+--J--------------+-+-J---------------+-+6-----+----------+-J------+----------+G-------+-------+--J--------+-------+-J---------+-------+7------+---+-------J-------+---+------J--------+---+-----J---------+---+----J----------+---+---J-----------+---+--J------------+---+-J-------------+---+8-------+------+---J--------+------+--J---------+------+-J----------+------+6-----+-----+------J------+-----+-----J-------J-----+----+-------J------+----+------J-------+----+-----J--------+----+----J---------+----+---J----------+----+--J-----------+----+-J------------+----+D------------++----J-------------++---J--------------++--J---------------++-J----------------
  ++5----+------------+H-----+----------+-J------+----------+G-------+-------+--J--------+-------+-J---------+-------+7------+---+-------J-------+---+------J--------+---+-----J---------+---+----J----------+---+---J-----------+---+--J------------+---+-J-------------+---+8-------+------+---J--------+------+--J---------+------+-J----------+------+6-----+-----+------J------+-----+-----J-------J-----+----+-------J------+----+------J-------+----+-----J--------+----+----J---------+----+---J----------+----+--J-----------+----+-J------------+----+C-----------+-+----J------------+-+---J-------------+-+--J--------------+-+-J---------------+-+5----+-----------+-J-----+-----------+H------+---------+-J-------+---------+C--------+--+------J---------+--+-----J----------+--+----J-----------+--+---J------------+--+--J-------------+--+-J--------------+--+7------+--------+--J-------+--------+-J--------+--------+5----+----J--------+-----+---J---------+-----+--J----------+-----+-J-----------+-----+E------------++----J-------------++---J--------------++--J---------------++-J----------------

3 Balls, Height 21

(L, Lbound, States) = (1266, 1266, 1330)

Complete: (1 pattern, 29 minutes)

inverse of:

  F511161111G111711111E1111711111F1711111A11111E11I111111111711111

3 Balls, Height 22

(L, Lbound, States) = (1469, 1470, 1540)

Type I Incomplete: (at least 4 patterns -- calculation not completed)

inverses of:

  I411411F1111111112I118111111511G011411F11111115111I1411411F111111115111
  I411411F111112011J11181111115111F11411F11111115111I1411411F111111115111
  I313131E1111111112E131E11111111711J01318111111E11111G111111E11111115111
  I313131E120111111F1131E111111117111I1318111111E11111G111111E11111115111
Type II patterns: calculation not performed


4 Balls


4 Balls, Height 5

(L, Lbound, States) = (5, 5, 5)

  55550

4 Balls, Height 6

(L, Lbound, States) = (12, 12, 15)

Complete: (1 pattern)
  +++1+-++1+4-

4 Balls, Height 7

(L, Lbound, States) = (30, 30, 35)

Complete: (1 pattern)
  +++1+--++3-++-+1+-++-6-+-++4--

4 Balls, Height 8

(L, Lbound, States) = (58, 60, 70)

Type I Incomplete: (26 patterns)
  +++3--+-++3--++-+1+--++-7-+--+6+--+-+1++--+-7-+5--+++-7---
  +++3--+-++1+--+-+1++--+-7-7+--++-7-+--++4--++-+3--+++-7---
  +++3--+-++1+--+-+1++--+-5-++-+1+--++-7-+--++2-+5--+++-7---
  +++2-+--++4--++-+1+--++-4-+-++1+--+-+1++--+-7-+5--+++-7---
  +++2-+--++2-+6--++-+2-+-++-7--+-++2-+-+-+2-++-+-2-+++-7---
  +++2-+--++2-+6--++-+2-+-++-7--+-++2-+-+-+11++-+-2-+++-7---
  +++2-+--++2-+6--++-+2-+-++-7--+-+37-+-+-+2-++-+-2-+++-7---
  +++2-+--++2-+1+-++--7-+-++-7--+-+31++-+-7--++-+3--+++-7---
  +++2-+--++2-+1+-++--6-+-++1+--+-+3-++-+-7--++-+3--+++-7---
  +++2-+--++1+-+--+5-+-++-7--+-+2++--+-7-+6--++-+3--+++-7---
  +++2-+--++1+-+--75-+-++1+--+-+1++--+-7-+6--++-+3--+++-7---
  +++1+---++5-+--++4--++-+1+--++-1+1+-++--7-+-++-7--+-++5---
  +++1+---++5-+--++2-+6--++-+2-+-++-7--+-++2-+-+-+2-++-+-5--
  +++1+---++5-+--++2-+1+-++--7-+-++-7--+-+31++-+-7--++-+6---
  +++1+---++5-+--++2-+1+-++--6-+-++1+--+-+3-++-+-7--++-+6---
  +++1+---++5-+--++1+-+--75-+-++1+--+-+1++--+-7-+6--++-+6---
  +++1+---++5-+--++1+-+--+5-+-++-7--+-+2++--+-7-+6--++-+6---
  +++1+---++3-+6--++-+1+--++-7-+--+3+-++--7-+-++-7--+-++5---
  +++1+---++3-+1+-++--7-+-++-7--+-+4+--++-7-+--++4--++-+6---
  +++1+---++3-+1+-++--7-+-++-2-++-+1+--++-7-+--++5--+-++5---
  +++1+---+6+-+--+6-+-+-+6--+-++1+--+-+6-+--++2-+6--++-+6---
  +++1+---+6+-+--+6-+-+-+15-+-++1+--+-+6-+--++2-+6--++-+6---
  +++1+---+6+-+--77-+-+-+6--+-++1+--+-+6-+--++2-+6--++-+6---
  ++3+-+--+6-+-+-+6--+-++1+--+-+6-+--++2-+6--++-+3--+++-7---
  ++3+-+--+6-+-+-+15-+-++1+--+-+6-+--++2-+6--++-+3--+++-7---
  ++3+-+--77-+-+-+6--+-++1+--+-+6-+--++2-+6--++-+3--+++-7---
Type II Incomplete: (18 patterns)
  +++3--+-++3--++-+1+--++-7-+--+6+--+-+1+17-+-7-+5--+++-7---
  +++3--+-++1+--+-+1++--+-7-+2-++4--++-+1+--++-7-7--+++-7---
  +++3--+-++1+--+-+1+17-+-7-+2-++4--++-+1+--++-7-7--+++-7---
  +++3--+-++1+--+-+1+17-+-7-7+--++-7-+--++4--++-+3--+++-7---
  +++3--+-++1+--+-+1+17-+-5-++-+1+--++-7-+--++2-+5--+++-7---
  +++2-+--++4--++-+1+--++-4-+-++1+--+-+1+17-+-7-+5--+++-7---
  +++2-+--++2-+1+-+17-6-+-++1+--+-+3-++-+-7--++-+3--+++-7---
  +++2-+--++1+-+--+5-+-++-7--+-+2+17-+-7-+6--++-+3--+++-7---
  +++1+---++5-+--++4--++-+1+--++-1+1+-+17-7-+-++-7--+-++5---
  +++1+---++5-+--++2-+6--++-+2-+-++-7--+-++2-+-+-+11++-+-5--
  +++1+---++5-+--++2-+6--++-+2-+-++-7--+-+37-+-+-+2-++-+-5--
  +++1+---++5-+--++2-+1+-+17-6-+-++1+--+-+3-++-+-7--++-+6---
  +++1+---++5-+--++1+-+--+5-+-++-7--+-+2+17-+-7-+6--++-+6---
  +++1+---++3-+6--++-+1+--++-7-+--+3+-+17-7-+-++-7--+-++5---
  +++1+---++3-+1+-+17-7-+-++-7--+-+4+--++-7-+--++4--++-+6---
  +++1+---++3-+1+-+17-7-+-++-2-++-+1+--++-7-+--++5--+-++5---
  +++1+---++1+1+--++-7-+--++4--+6-+1+-++--7-+-++-7--+-++5---
  +++1+---++1+1+--++-7-+--++4--+6-+1+-+17-7-+-++-7--+-++5---

4 Balls, Height 9

(L, Lbound, States) = (112, 112, 126)

Complete: (5 patterns)
  +++4---+-++1+---+-+5-+--++-8--+--++5---++-+1+---++-8-+---++5--+-+-+1+--+-+-8-+--+-+2-++--+-8--++--+6---+++-8----
  +++3--+--++1+--+--+7-+--+-+1+-+--+-8-+-+--+7--+-+-+7---+-++1+---+-+7-+---++2-++---+6--++-+-8---++-+4---+++-8----
  +++2-+---++5--+-+-+1+--+-+-8-+--+-+4--++-+-8---++-+2-+--++-8--+--++6---+-++1+---+-+3-++--+-8--++--+6---+++-8----
  +++2-+---++1+-+---+7-+-+--+7--+-+-+1+--+-+-8-+--+-+5--+-++-8---+-++4---++-+2-+--++-8--+--++3--++--+6---+++-8----
  +++1+----++6-+---++2-++---+6--++-+-8---++-+2-+--++-8--+--++2-+-+--+7--+-+-+1+--+-+-8-+--+-+5--+-++-8---+-++6----

4 Balls, Height 10

(L, Lbound, States) = (188, 188, 210)

Complete: (9 patterns, 11 hours)
  +++4---+--++1+---+--+3-++--+--9--++--+-9---++--+3--+-++--9---+-++-9----+-++3--+--+-+2-+-9--+-+--+2-+-+-+--9--+-+-+-9---+-+-+4---++-+-9----++-+2-+---++-9--+---++3--+6---+++--9----+++-9-----
  +++3--+---++1+--+---+7-+--+-+-9--+--+-+2-+-9--+-+--+8---+-+-+1+---+-+-9-+---+-+4--++--+-9---++--+2-+--++--9--+--++-9---+--++7----+-++1+----+-+8-+----++4--+7---++-+-9----++-+5----+++-9-----
  +++2-+----++4--+8---++--+1+---++--9-+---++-9--+---++6---+-+-+1+---+-+-9-+---+-+6--+--++-9---+--++2-+--+--+1+-+--+--9-+-9--+-+--+7---+-++-9----+-++3--+--+-+5---++-+-9----++-+5----+++-9-----
  +++2-+----++4--+7---++-+-9----++-+4---+-++-9----+-++4---+-+-+1+---+-+-9-+---+-+8--+---++1+--+---+8-+--+--+7--+--++-9---+--++3--+-+--+1+--9-+--+-+-9--+--+-+3--++--+-9---++--+7----+++-9-----
  +++2-+----++4--+7---++-+-9----++-+4---+-++-9----+-++4---+-+-+1+---+-+-9-+---+-+8--+---++1+--+---+6-+--++--9--+--++-9---+--++3--+-+--+1+--9-+--+-+-9--+--+-+3--++--+-9---++--+7----+++-9-----
  +++2-+----++4--+7---++-+-9----++-+2-+---++-9--+---++7---+--++1+---+--+3-++--+--9--++--+-9---++--+3--+-++--9---+-++-9----+-++3--+--+-+2-+-9--+-+--+2-+-+-+--9--+-+-+-9---+-+-+6----+++-9-----
  +++2-+----++4--+7---++-+-9----++-+2-+---++-9--+---++6---+-+-+1+---+-+-9-+---+-+6--+--++-9---+--++2-+--+--+1+-+--+--9-+-9--+-+--+7---+-++-9----+-++3--+--+-+3--++--+-9---++--+7----+++-9-----
  +++1+-----++7-+----++4--+8---++--+1+---++--9-+---++-9--+---++6---+-+-+1+---+-+-9-+---+-+6--+--++-9---+--++2-+--+--+1+-+--+--9-+-9--+-+--+7---+-++-9----+-++3--+--+-+5---++-+-9----++-+8-----
  +++1+-----++7-+----++4--+7---++-+-9----++-+2-+---++-9--+---++6---+-+-+1+---+-+-9-+---+-+4--++--+-9---++--+2-+--++--9--+--++-9---+--++3--+-+--+1+--9-+--+-+-9--+--+-+6---+-++-9----+-++7-----

4 Balls, Height 11

(L, Lbound, States) = (300, 300, 330)

Complete: (144 patterns)

inverses of:

  5A2681117182A1229A1112A1283131
  5A27319113A22A312A129128116151
  5A415A118131719314A15191811611
  5A415A118131814A15191319711611
  5A51419A1122A14173191491811611
  5A518131814A12A231718118911511
  6A224A12A12911711818312A273131
  6A2284118182A11512A612A1711611
  6A24172A114A12A12911315A163141
  6A241731914A129128112A61811611
  6A24192911315A14812A114A161141
  6A2613188131913A26118191811611
  6A2713181929118112A414A1261611
  6A27131914A131929118112A246131
  6A313A228131619618118191811611
  6A3192316181727117A12A12911511
  6A8112A114A125161619419A111511
  6A81131814A12A2A111317A1261611
  74A12931911418A171117199112611
  788111618A1317181189112A126411
  797111619293181181913192812611
  7A22A12911319512A318312A163141
  7A22A13191611713A239312A171231
  7A22A13191611713A7122A12831611
  7A31413A259112A17131914A171131
  7A31418911316A17131914A1711611
  7A31419A1122A12841161791811611
  7A318131616A12A231718118911511
  7A318191113A2A4112A12A23171251
  7A319122A128411713A612A1711611
  7A319122A151918118113A23841151
  7A3191318191811811771161926411
  83A319122A151918118113A2741151
  8491319A1131912971116199131611
  884116194182A11518191319711611
  884117192A12911319418318171611
  884117193183181717118A12911511
  88411814A151918118113A51912511
  884118183181717118A14118911511
  89312A151916118194113A51812611
  8931318A13191611719314A1712611
  8931711618A13191319314A1712611
  893181181913192297111619712611
  893181181916118194116711881411
  8931911418A12611719314A1712611
  8931911418A14118611814A1712611
  894118141941929117117192812611
  899111161829A1112A151299112611
  8A2A1112A1413A81131617A1261611
  8A2A11131841991131814A15171611
  8A3131929128116161951719117411
  8A313193193151619A131291812611
  8A3131971171189128118151817411
  8A3181171189128118151719317411
  8A318118113A518131814A15181511
  8A318118113A519122A15151817411
  8A51113A248131819A1112A1517131
  93491319A113191297111619913131
  936281189112912931419A12811151
  938317118912711819319131961141
  938318113A519122A1419319161151
  9383181172A1418A111418A1261151
  9384116194182A1151819131971131
  9384117192A1291131941831817131
  939312A151916118194113A5181231
  93931318A13191611719314A171231
  93931711618A13191319314A171231
  939318118191319229711161971231
  93931911418A12611719314A171231
  93931911418A14118611814A171231
  9394112A612A128129113A26171151
  939411814194192911711719281231
  9399111161829A1112A15129911231
  93A2A1112A1413A81131617A126131
  93A2A11131841991131814A1517131
  93A313193193151619A13129181231
  94418911811814197131913A271131
  94418911811814197131913A811131
  948128118911319419315191941141
  948128118911711819314192941141
  948131914A1313A2618112A6181131
  949123192A31319611817191173151
  949123194193191319611619183131
  949129114194192319611619183131
  94A129113192841171931831817131
  94A129117117193183181419283131
  94A131419283181189117118183141
  94A131519183181189113194183141
  94A131718118911319284118183141
  94A141189113192841181831817131
  94A141189113194183181519183131
  94A141189117118183181419283131
  952A128129113A7117116192941141
  95611818A111418A141172A1283131
  9581171188131914A1313A71181141
  959112A17131713A413A22A1317131
  95911318619113A27131914A161141
  95911711617A128129113A22941141
  959118112A414A12619113A2713151
  95911811812A313A27117118813151
  95911811812A313A81117118813151
  962A114193193191611616A1283131
  96319141891131941731914A171131
  963191419319291131951519183131
  964117A12416A11631819291181141
  964118419319291181181519183131
  9681117182A1229A111316A1283131
  968111719229291181181419283131
  97319113A224A129128112A6161151
  97319114A12A51113A519129115151
  9741161925A1141931831819181131
  97411713A512A2A1122A1249181131
  97411813A224A129128112A6181131
  97411818319141891131924A171131
  992411819231929129114192941141
  992411819319131929123192941141
  9A251115914A191129113A71181141
  9A3128118191319319611159183131
  9A411811812A81181115913A271131
  9A411811812A81181115913A811131
  A336281189112912931419A1281112
  A338318113A519122A141931916112
  A3383181172A1418A111418A126112
  A3384117193182A115181918117113
  A3384118182A115181913197117113
  A3394112A612A128129113A2617112
  A33A318118117A118131814A151413
  A349123192A3131961181719117312
  A34A12611817281172A1292A111413
  A358118117A118131814A12A411413
  A359112A17131716A113A22A131413
  A359118112A414A12619113A271312
  A35911811812A313A2711711881312
  A35911811812A313A8111711881312
  A37319113A224A129128112A616112
  A37319113A22A312A1291281161613
  A37319114A12A51113A51912911512
  A39313191931811819131931961113
  A4294112A252A128129113A7117112
  A42A41171911791113A24912811612
  A42A41171911791113A262A1151612
  A44182A115181918118113A2384112
  A4A1312918122A13A3131931931413
  A529128112A238319113A251916112

4 Balls, Height 12

(L, Lbound, States) = (452, 452, 495)

Complete: (45 patterns, 97 minutes)

inverses of:

  8B22313B7112B12B12A11131A7131918131A1731611
  8B22319B11131A2B14118131A7131918131A1731611
  8B23191231A29241171A2A141181A1319B111811611
  8B23191231A292411819B11131A2A141181A1711611
  93A2B11131A2A141181A131A3191811161AA1231611
  94B12319B11131A61171A118411616B1712B1171411
  9728111891911181A17119119B11161171A31931511
  9741161A51913181A17119119B11131A315B1171411
  9741161A713181A1319B1118118117B112B23181411
  9741191681117A17119119B11131AB1141191912511
  99241161A519131A151A17119119B11131A31931511
  9A23131A713181A131A3141A2B12B11161191822611
  9A31911181A12812A11841171A5119B111511961511
  9B22B11131A611418B12314B1712B11713191831611
  9B41131A2A14119161A11823181A2B113141A712511
  9B41131A318317119B141181A1191316181A2911411
  9B41131A318317119B141181A1191316181AA111411
  9B4118112B173131A4182A1118B11141A251A161141
  9B411811911931A15117A11914119A1411619182411
  A33A2B11131A2A141181A131A3191811161AA123131
  A3728111891911181A17119119B11131A3193171151
  A39231A114A1291271171A5119B1115119A1A111141
  A39231A11571171A5119B1112A12914119A1A111141
  A39231A1193171171A5119B111511951A1291911141
  A394119119B1112A1291231A41841171A2A1A111141
  A3A23131A713181A131A3141A2B12B1116119182231
  A3B22B1112A1291231A4183191173171A2A1A111141
  A3B22B11131A611418B12314B1712B1171319183131
  A4B12B1116119193191141A29231811931A31913141
  A531A3191291141A41A2B11131A2A141161A1923131
  A57119119B11131A3193191151A1728111891911141
  A5B113171A11823181A3191231A2B41131A2A141141
  A6B11131A3193131A29241181A319131A151A171131
  A6B11131A31A411418B12314B1712B117131A173131
  A6B11131A611418B12314B12A312B11712A11841151
  A73131A2A313181A131A3141A2B12B1116119182231
  A73191141A41A2B11131A241A2291911161A1923131
  A73191141A7131A1419B11131A318231A14B1271131
  A731A11914117B122B3161161A172A1113B71181131
  A8241171A2A14119191291141A23B22319B11181131
  A82411819B11131A2A14119191291141A23B2271131
  B33728111891911181A17119119B11131A319317112
  B36B11131A611418B12314B12A312B11712A1184112
  B42B41131A3182A1118B11151A151A17112B1731313
  B52A1A11112B2392319113B241A2B1112A129127112

4 Balls, Height 13

(L, Lbound, States) = (660, 660, 715)

Complete: (at least 245 patterns -- calculation not completed)

partial list -- inverses of:

  8A8111171BB11411911A318181119C131B11A11181181B1B1171111
  5C8141191B11711811A2C1411A17111915C11A131A1114C18171111
  5C51A1411811A2C131B11711191A41191911A1181A1114C18171111
  8A8111181AC1119111711AA131911192C1711191911811A1A171111
  882A11199111811AC118111161B515191B11A112A1151B1B1271111
  8C312B131B11A11911191B1811191193141BB12511171B2B1271111
  8C312B131B11A11811171B2B1511191B1811191193141BB13181111
  5C515191811191B31B11A11191191811811A811A1114C1519181111
  6C7119112A114C12C1312C11511A3191811161BC151112A19181111
  8A8111171B261B11A11911181B1711A1181A1119911171199181111
  6C261711911AC1112C11711811A1A128111617C125181B111881111
  6C711911A1114C151A128111617C12C1312C11711A1161A11881111

5 Balls


5 Balls, Height 6

(L, Lbound, States) = (6, 6, 6)

  666660

5 Balls, Height 7

(L, Lbound, States) = (18, 18, 21)

Complete: (1 pattern)
  ++++1+-+++1++-++4-

5 Balls, Height 8

(L, Lbound, States) = (49, 49, 56)

Complete: (3 patterns)
  ++++2-+-+++1+-+-++1++-+-+6-++-++2-+++-+2-++++-7--
  ++++1+--+++4-+-+++1+-+-++1++-+-+6-++-++2-+++-+6--
  ++++1+--+++3-++-++1+-++-+6-+-+++1+-+-++3-+++-+6--

5 Balls, Height 9

(L, Lbound, States) = (112, 112, 126)

Complete: (5 patterns)
  ++++3--+-+++1+--+-++4-+-++-+1+-+-++-8-+-+-++2-++-+-+7--++-++1+--++-+7-+--+++1+-+--++3-+++--+7--+++-+3--++++-8---
  ++++1+---+++5-+--+++1+-+--++3-+++--+7--+++-+2-+-+++-8--+-+++2-+-+-++2-++-+-+1+-++-+-8-+-++-+2-++-++-8--++-++6---
  ++++1+---+++3-++--++6--++-++1+--++-+7-+--+++5--+-+++1+--+-++4-+-++-+1+-+-++-8-+-+-++2-++-+-+2-+++-+-8--+++-+7---
  ++++1+---+++3-++--++1+-++--+7-+-++-+1+-+-++-8-+-+-++4--+++-+1+--+++-8-+--+++4--++-++1+--++-+4-+-+++-8--+-+++5---
  ++++1+---+++3-++--++1+-++--+6-+-+++-8--+-+++3--++-++1+--++-+7-+--+++1+-+--++5-+-++-+1+-+-++-8-+-+-++4--+++-+7---

5 Balls, Height 10

(L, Lbound, States) = (225, 226, 252)

Type I Incomplete: (752 patterns, 4.5 minutes)

partial list -- inverses of:

  9939229139931392939318414
  9939229139481392939318414
  9933931892292681293958113
  9933922962916292939318414
  9933922939248188129295314
  9933891139393491691297313
  9933891139393491397291613
  9793181841882491494918313
  9793171691494913991296114
  9793129629282491494918313
  9792911393697117913897112
  9792911393692617913897112
  9792281395813924939292612
  9792271881491493929318414
  9792271691692293929318414

  993922913993139293931A71414
  993922913993139293931895014
  993922913948139293931A71414
  993922913948139293931895014
  993393189A11292681293958113
  993393189293092681293958113
  993392296291629293931A71414
  993392296291629293931895014
  99339229392481A718129295314
  993392293924818990129295314
  9793181A7141882491494918313
  979318189501882491494918313
  9793129A5129282491494918313
  979312969309282491494918313
  979228139581392493929A11612
Type II Incomplete: (86 patterns, 28 minutes)
  ++++4---+-+++1+---+-++7-+---+++5--+-+-++1+--+-+-+1+19-+-+-9-++--+-+6--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++4--++-+-+3--+++-+-9---+++-+2-+--+++-9--+--+++3--++--++1+--++--+8-+--++-+1+-+--++-9-+-+--++4--+++--+7---++++-9----
  ++++4---+-+++1+---+-++7-+---+++2-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+1+--++-+-9-+--++-+4--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++7--+--+++2-+-+--++2-++-+--+2-+++-+--9--+++-+-9---+++-+4---++++-9----
  ++++4---+-+++1+---+-++7-+---+++1+-+---++1++-+---+8-++-+--+8--++-+-+8---++-++3--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++6-+--++-+1+-+--++-9-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+8---+++-+4---++++-9----
  ++++4---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+8---+++-+1+---+++-9-+---+++6--+--+++1+--+--++3-++-+--+7--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++4--++-+-+6---++++-9----
  ++++4---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++3-++-+--+7--++-++-9---++-++4---+++-+1+---+++-9-+---+++2-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+6---++++-9----
  ++++4---+-+++1+---+-++1++---+-+8-++---++6--++-+-+1+--++-+-9-+--++-+2-++--++-9--++--++7---++-++1+---++-+8-+---+++6--+--+++1+--+--++7-+--+-++1+-+--+-+8-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+5--+++-+-9---+++-+4---++++-9----
  ++++4---+-+++1+---+-++1++---+-+6-++--++-9--++--++7---++-++1+---++-+8-+---+++2-++---++6--++-+-+1+--++-+-9-+--++-+8--+--+++1+--+--++7-+--+-++1+-+--+-+8-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+5--+++-+-9---+++-+4---++++-9----
  ++++4---+-+++1+---+-++1++---+-+6-++--++-9--++--++7---++-++1+---++-+8-+---+++1+-+---++5-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+1+--++-+-9-+--++-+8--+--+++1+--+--++7-+--+-++1+-+--+-+8-+-+--++4--+++--+8---+++-+4---++++-9----
  ++++4---+-+++1+---+-++1++---+-+6-++--++-9--++--++7---++-++1+---++-+8-+---+++1+-+---++5-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+1+--++-+-9-+--++-+8--+--+++1+--+--++7-+--+-++1+-+--+-+3-+++--+-9--+++--+8---+++-+4---++++-9----
  ++++4---+-+++1+---+-++1++---+-+6-++--++-9--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+1+--++-+-9-+--++-+4--++-++-9---++-++4---+++-+1+---+++-9-+---+++6--+--+++1+--+--++7-+--+-++1+-+--+-+8-+-+--++4--+++--+7---++++-9----
  ++++4---+-+++1+---+-++1++---+-+6-++--++-9--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+1+--++-+-9-+--++-+4--++-++-9---++-++4---+++-+1+---+++-9-+---+++6--+--+++1+--+--++7-+--+-++1+-+--+-+3-+++--+-9--+++--+7---++++-9----
  ++++4---+-+++1+---+-++1++---+-+5-++-+-+-9--++-+-+8---++-++1+---++-+8-+---+++2-++---++7--++--++1+--++--+8-+--++-+8--+--+++1+--+--++7-+--+-++1+-+--+-+8-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+5--+++-+-9---+++-+4---++++-9----
  ++++3--+--+++1+--+--++7-+--+-++4--++-+-+2-+-++-+-9--+-++-+8---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++2-++-+--+7--++-++-9---++-++4---+++-+1+---+++-9-+---+++5--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+7---++++-9----
  ++++3--+--+++1+--+--++6-+--++-+1+-+--++-9-+-+--++2-++-+--+7--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++4--++-+-+3--+++-+-9---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+3--++++--9---++++-9----
  ++++3--+--+++1+--+--++4-+-++--+1+-+-+19-9-+-+-++-9--+-+-++5---+++-+3--+-+++-9---+-+++4---++-++1+---++-+8-+---+++1+-+---++7-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+2-++--++-9--++--++3--+++--+7---++++-9----
  ++++3--+--+++1+--+--++3-++-+--+8--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++2-+--+-++1+-+--+-+8-+-+--++6--+-++-+3--++-++-9---++-++4---+++-+1+---+++-9-+---+++5--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+7---++++-9----
  ++++3--+--+++1+--+--++3-++-+--+7--++-++-9---++-++4---+++-+1+---+++-9-+---+++2-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+6---++++-9----
  ++++3--+--+++1+--+--++3-++-+--+7--++-++-9---++-++4---+++-+1+---+++-9-+---+++2-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++2-+--+-++1+-+--+-+8-+-+--++6--+-++-+5---++++-9----
  ++++3--+--+++1+--+--++3-++-+--+7--++-++-9---++-++2-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+3--+++-+-9---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+3--++++--9---++++-9----
  ++++2-+---+++6--+--+++1+--+--++6-+--++-+1+-+--++-9-+-+--++2-++-+--+7--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++4--++-+-+3--+++-+-9---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+7---++++-9----
  ++++2-+---+++6--+--+++1+--+--++3-++-+--+7--++-++-9---++-++2-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+3--+++-+-9---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+7---++++-9----
  ++++2-+---+++5--+-+-++1+--+-+-+1+19-+-+-9-++--+-+5--+++-+-9---+++-+3--+-+++-9---+-+++4---++-++1+---++-+5-+--+++-9--+--+++2-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+2-++--++-9--++--++3--+++--+7---++++-9----
  ++++2-+---+++5--+-+-++1+--+-+-+1+19-+-+-9-++--+-+5--+++-+-9---+++-+2-+--+++-9--+--+++6---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+8---++-++1+---++-+3-++--++-9--++--++3--+++--+7---++++-9----
  ++++2-+---+++5--+-+-++1+--+-+-+1+19-+-+-9-++--+-+5--+++-+-9---+++-+2-+--+++-9--+--+++2-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++4---++-++1+---++-+3-++--++-9--++--++3--+++--+7---++++-9----
  ++++2-+---+++2-++---++7--++--++1+--++--+8-+--++-+8--+--+++2-+-+--++1+-+-+--+3-+++-+--9--+++-+-9---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+6--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++4--++-+-+6---++++-9----
  ++++2-+---+++2-++---++7--++--++1+--++--+7-+--+++-9--+--+++6---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+6--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++4--++-+-+3--+++-+-9---+++-+4---++++-9----
  ++++2-+---+++2-++---++2-+++---+7--+++-+-9---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+6--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++6-+--++-+1+-+--++-9-+-+--++2-++-+--+8--++-+-+6---++++-9----
  ++++2-+---+++2-++---++2-+++---+7--+++-+-9---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+6--++-++-9---++-++2-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++3-++-+--+8--++-+-+6---++++-9----
  ++++2-+---+++1+-+---++7-+-+--++6--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++4-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++4---++-++1+---++-+3-++--++-9--++--++3--+++--+8---+++-+4---++++-9----
  ++++2-+---+++1+-+---++7-+-+--++6--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++3-++-+--+8--++-+-+1+--++-+-9-+--++-+4--++-++-9---++-++4---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+7---++++-9----
  ++++2-+---+++1+-+---++7-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+8--+--+++1+--+--++4-+-++--+1+-+-+19-9-+-+-++-9--+-+-++5---+++-+3--+-+++-9---+-+++4---++-++1+---++-+3-++--++-9--++--++3--+++--+7---++++-9----
  ++++2-+---+++1+-+---++7-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+8--+--+++1+--+--++3-++-+--+7--++-++-9---++-++4---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+7---++++-9----
  ++++2-+---+++1+-+---++5-+-++--+1+-+-+19-9-+-+-++-9--+-+-++5---+++-+3--+-+++-9---+-+++4---++-++1+---++-+5-+--+++-9--+--+++2-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+2-++--++-9--++--++3--+++--+7---++++-9----
  ++++2-+---+++1+-+---++5-+-++--+1+-+-+19-9-+-+-++-9--+-+-++5---+++-+2-+--+++-9--+--+++6---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+8---++-++1+---++-+3-++--++-9--++--++3--+++--+7---++++-9----
  ++++2-+---+++1+-+---++5-+-++--+1+-+-+19-9-+-+-++-9--+-+-++5---+++-+2-+--+++-9--+--+++2-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++4---++-++1+---++-+3-++--++-9--++--++3--+++--+7---++++-9----
  ++++2-+---+++1+-+---++3-+++---+8--+++--+8---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+6--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++6-+--++-+1+-+--++-9-+-+--++2-++-+--+8--++-+-+6---++++-9----
  ++++2-+---+++1+-+---++3-+++---+8--+++--+8---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+6--++-++-9---++-++2-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++3-++-+--+8--++-+-+6---++++-9----
  ++++2-+---+++1+-+---++1++-+---+8-++-+--+8--++-+-+1+--++-+-9-+--++-+8--+--+++1+--+--++7-+--+-++1+-+--+-+8-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+8---+++-+3--+-+++-9---+-+++4---++-++3--+-++-+5---++++-9----
  ++++2-+---+++1+-+---++1++-+---+8-++-+--+8--++-+-+1+--++-+-9-+--++-+8--+--+++1+--+--++7-+--+-++1+-+--+-+8-+-+--++4--+++--+8---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++7---++-++3--+-++-+5---++++-9----
  ++++2-+---+++1+-+---++1++-+---+8-++-+--+8--++-+-+1+--++-+-9-+--++-+8--+--+++1+--+--++7-+--+-++1+-+--+-+3-+++--+-9--+++--+8---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++7---++-++3--+-++-+5---++++-9----
  ++++2-+---+++1+-+---++1++-+---+8-++-+--+8--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++2-+--+-++1+-+--+-+8-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+8---+++-+2-+--+++-9--+--+++5---++-++3--+-++-+5---++++-9----
  ++++2-+---+++1+-+---++1++-+---+7-++-+-+-9--++-+-+8---++-++3--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++6-+--++-+2-++--++-9--++--++6---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+2-+++--+-9--+++--+7---++++-9----
  ++++2-+---+++1+-+---++1++-+---+7-++-+-+-9--++-+-+8---++-++3--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++1++--+--+7-++--++-9--++--++6---+++-+3--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+2-+++--+-9--+++--+7---++++-9----
  ++++1+----+++6-+---+++2-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+1+--++-+-9-+--++-+4--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++7--+--+++2-+-+--++2-++-+--+2-+++-+--9--+++-+-9---+++-+3--+-+++-9---+-+++6----
  ++++1+----+++6-+---+++2-++---++7--++--++1+--++--+7-+--+++-9--+--+++6---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+6--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++4--++-+-+3--+++-+-9---+++-+8----
  ++++1+----+++6-+---+++2-++---++6--++-+-+2-+-++-+-9--+-++-+3--++-++-9---++-++2-+--++-+1+-+--++-9-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+5--+++-+-9---+++-+2-+--+++-9--+--+++3--++--++1+--++--+4-+-+++--9--+-+++-9---+-+++6----
  ++++1+----+++6-+---+++2-++---++1+-++---+7-+-++-+-9--+-++-+3--++-++-9---++-++2-+--++-+1+-+--++-9-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+5--+++-+-9---+++-+2-+--+++-9--+--+++3--++--++1+--++--+4-+-+++--9--+-+++-9---+-+++6----
  ++++1+----+++6-+---+++1+-+---++7-+-+--++6--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++4-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++4---++-++1+---++-+3-++--++-9--++--++3--+++--+8---+++-+8----
  ++++1+----+++6-+---+++1+-+---++5-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+2-+-++-+-9--+-++-+3--++-++-9---++-++4---+++-+2-+--+++-9--+--+++3--++--++1+--++--+8-+--++-+1+-+--++-9-+-+--++4--+++--+2-+-+++--9--+-+++-9---+-+++6----
  ++++1+----+++6-+---+++1+-+---++5-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+2-+-++-+-9--+-++-+3--++-++-9---++-++2-+--++-+2-++--++-9--++--++3--+++--+8---+++-+2-+--+++-9--+--+++2-+-+--++1+-+-+--+5-+-+++--9--+-+++-9---+-+++6----
  ++++1+----+++6-+---+++1+-+---++5-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+2-+-++-+-9--+-++-+3--++-++-9---++-++2-+--++-+1+-+--++-9-+-+--++4--+++--+8---+++-+2-+--+++-9--+--+++3--++--++1+--++--+4-+-+++--9--+-+++-9---+-+++6----
  ++++1+----+++6-+---+++1+-+---++1++-+---+8-++-+--+8--++-+-+8---++-++3--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++6-+--++-+1+-+--++-9-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+8---+++-+3--+-+++-9---+-+++6----
  ++++1+----+++5-+--+-++7--+--+++6---+-+++1+---+-++7-+---+++2-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+2-+-++-+-9--+-++-+3--++-++-9---++-++2-+--++-+1+-+--++-9-+-+--++2-++-+--+2-+++-+--9--+++-+-9---+++-+8----
  ++++1+----+++5-+--+-++7--+--+++5---++-++1+---++-+8-+---+++2-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+2-+-++-+-9--+-++-+8---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++2-++-+--+2-+++-+--9--+++-+-9---+++-+8----
  ++++1+----+++5-+--+-++7--+--+++3--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++2-++---++6--++-+-+2-+-++-+-9--+-++-+3--++-++-9---++-++2-+--++-+1+-+--++-9-+-+--++2-++-+--+2-+++-+--9--+++-+-9---+++-+8----
  ++++1+----+++5-+--+-++7--+--+++3--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++2-++---++1+-++---+7-+-++-+-9--+-++-+3--++-++-9---++-++2-+--++-+1+-+--++-9-+-+--++2-++-+--+2-+++-+--9--+++-+-9---+++-+8----
  ++++1+----+++5-+--+-++4--++-+-+2-+-++-+-9--+-++-+8---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+8---+++-+1+---+++-9-+---+++6--+--+++1+--+--++3-++-+--+7--++-++-9---++-++7----
  ++++1+----+++4-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+8---+++-+1+---+++-9-+---+++6--+--+++1+--+--++3-++-+--+7--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++6----
  ++++1+----+++4-+-+--++6--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++4-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++1+-+---++1++-+---+7-++-+-+-9--++-+-+8---++-++2-+--++-+2-++--++-9--++--++3--+++--+8---+++-+8----
  ++++1+----+++4-+-+--++6--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++3-++-+--+7--++-++-9---++-++4---+++-+1+---+++-9-+---+++2-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++3--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++6----
  ++++1+----+++4-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++3--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++3--+++--+8---+++-+1+---+++-9-+---+++6--+--+++1+--+--++3-++-+--+7--++-++-9---++-++7----
  ++++1+----+++4-+-+--++2-++-+--+8--++-+-+1+--++-+-9-+--++-+4--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++4-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++2-++---++2-+++---+7--+++-+-9---+++-+8----
  ++++1+----+++4-+-+--++2-++-+--+8--++-+-+1+--++-+-9-+--++-+4--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++4-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++1+-+---++3-+++---+8--+++--+8---+++-+8----
  ++++1+----+++4-+-+--++2-++-+--+7--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+8--+--+++1+--+--++4-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++2-++---++2-+++---+7--+++-+-9---+++-+8----
  ++++1+----+++4-+-+--++2-++-+--+7--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+8--+--+++1+--+--++4-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++1+-+---++3-+++---+8--+++--+8---+++-+8----
  ++++1+----+++3-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++6--+--+++1+--+--++6-+--++-+1+-+--++-9-+-+--++2-++-+--+7--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++4--++-+-+3--+++-+-9---+++-+8----
  ++++1+----+++3-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++6--+--+++1+--+--++3-++-+--+7--++-++-9---++-++2-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+3--+++-+-9---+++-+8----
  ++++1+----+++3-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++1+-+---++7-+-+--++6--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++3-++-+--+8--++-+-+1+--++-+-9-+--++-+4--++-++-9---++-++4---+++-+8----
  ++++1+----+++3-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++1+-+---++7-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+8--+--+++1+--+--++3-++-+--+7--++-++-9---++-++4---+++-+8----
  ++++1+----+++3-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++5---+++-+1+---+++-9-+---+++6--+--+++1+--+--++7-+--+-++4--++-+-+2-+-++-+-9--+-++-+8---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++2-++-+--+7--++-++-9---++-++7----
  ++++1+----+++3-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++5---+++-+1+---+++-9-+---+++6--+--+++1+--+--++3-++-+--+8--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++2-+--+-++1+-+--+-+8-+-+--++6--+-++-+3--++-++-9---++-++7----
  ++++1+----+++3-++---++7--++--++1+--++--+8-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+8---++-++1+---++-+5-+--+++-9--+--+++6---+-+++1+---+-++7-+---+++5--+-+-++1+--+-+-+1+19-+-+-9-++--+-+5--+++-+-9---+++-+8----
  ++++1+----+++3-++---++7--++--++1+--++--+8-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+8---++-++1+---++-+5-+--+++-9--+--+++6---+-+++1+---+-++7-+---+++1+-+---++5-+-++--+1+-+-+19-9-+-+-++-9--+-+-++5---+++-+8----
  ++++1+----+++3-++---++7--++--++1+--++--+8-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+3--+++-+-9---+++-+2-+--+++-9--+--+++6---+-+++1+---+-++7-+---+++5--+-+-++1+--+-+-+1+19-+-+-9-++--+-+6--++-++-9---++-++7----
  ++++1+----+++3-++---++7--++--++1+--++--+7-+--+++-9--+--+++6---+-+++1+---+-++7-+---+++5--+-+-++1+--+-+-+1+19-+-+-9-++--+-+6--++-++-9---++-++2-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+3--+++-+-9---+++-+8----
  ++++1+----+++3-++---++7--++--++1+--++--+7-+--+++-9--+--+++6---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+8---++-++1+---++-+8-+---+++5--+-+-++1+--+-+-+1+19-+-+-9-++--+-+5--+++-+-9---+++-+8----
  ++++1+----+++3-++---++7--++--++1+--++--+7-+--+++-9--+--+++6---+-+++1+---+-++5-+--++-+1+-+--++-9-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+8---++-++1+---++-+8-+---+++1+-+---++5-+-++--+1+-+-+19-9-+-+-++-9--+-+-++5---+++-+8----
  ++++1+----+++3-++---++7--++--++1+--++--+7-+--+++-9--+--+++2-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++4---++-++1+---++-+8-+---+++5--+-+-++1+--+-+-+1+19-+-+-9-++--+-+5--+++-+-9---+++-+8----
  ++++1+----+++3-++---++7--++--++1+--++--+7-+--+++-9--+--+++2-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+5--+-+++-9---+-+++4---++-++1+---++-+8-+---+++1+-+---++5-+-++--+1+-+-+19-9-+-+-++-9--+-+-++5---+++-+8----
  ++++1+----+++3-++---++6--++-+-+2-+-++-+-9--+-++-+3--++-++-9---++-++4---+++-+1+---+++-9-+---+++6--+--+++1+--+--++6-+--++-+1+-+--++-9-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++1+--++--+4-+-+++--9--+-+++-9---+-+++6----
  ++++1+----+++3-++---++6--++-+-+1+--++-+-9-+--++-+2-++--++-9--++--++7---++-++1+---++-+8-+---+++1+-+---++7-+-+--++6--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++4-+-++--+1+-+-+19-9-+-+-++-9--+-+-++5---+++-+3--+-+++-9---+-+++6----
  ++++1+----+++3-++---++1+-++---+8-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++4--++--++1+--++--+8-+--++-+4--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++7--+--+++2-+-+--++1+-+-+--+3-+++-+--9--+++-+-9---+++-+8----
  ++++1+----+++3-++---++1+-++---+8-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++4--++--++1+--++--+3-++-++--9--++-++-9---++-++3--+-++-+1+--+-++-9-+--+-++7--+--+++2-+-+--++1+-+-+--+3-+++-+--9--+++-+-9---+++-+8----
  ++++1+----+++3-++---++1+-++---+7-+-++-+-9--+-++-+3--++-++-9---++-++4---+++-+1+---+++-9-+---+++6--+--+++1+--+--++6-+--++-+1+-+--++-9-+-+--++7--+-+-++1+--+-+-+1+19-+-+-9-++--+-+8--++--++1+--++--+4-+-+++--9--+-+++-9---+-+++6----
  ++++1+----+++1++----++7-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++1+-+---++7-+-+--++6--+-++-+1+--+-++-9-+--+-++7--+--+++1+--+--++3-++-+--+8--++-+-+1+--++-+-9-+--++-+4--++-++-9---++-++7----
  ++++1+----+++1++----++7-++---++7--++--++2-+-++--+1+-+-+19-9-+-+-++-9--+-+-++7---+-+++1+---+-++7-+---+++1+-+---++7-+-+--++6--+-++-+1+--+-++-9-+--+-++4--++-+-+1+--++-+-9-+--++-+8--+--+++1+--+--++3-++-+--+7--++-++-9---++-++7----

5 Balls, Height 11

(L, Lbound, States) = (420, 420, 462)

Complete: (59346 patterns, 30 hours)

partial list -- inverses of:

  6A3A52A12A2929127199137A114A3AA13191913561
  6A5618A12A292912A139A27118188A11813AA16411
  6A5A1722A14A3A2418A161918A122A39413A718241
  7A62A163193842A2942A2A139318A1619199181161
  9A531881915199619118A2A1519182A318A2711661
  A4A429318A17181918812719923A22A53197A11613
  A6A22A711813A394A12619913A3194A123A3951712
  A73A319418A14174A1934A12A82317A17A12A16314
  A83A222A3A2529182A22A3A3192A1712A2A4415714
  A8A2318184199413A248A222A4A13A22A2A2A17112

6 Balls


6 Balls, Height 7

(L, Lbound, States) = (7, 7, 7)

  7777770

6 Balls, Height 8

(L, Lbound, States) = (24, 24, 28)

Complete: (1 pattern)
  +++++1+-++++1++-+++1++5-

6 Balls, Height 9

(L, Lbound, States) = (74, 74, 84)

Complete: (1 pattern)
  +++++1+--++++3-++-+++1+-++-++1+1+++-++-8-+++-++2-++++-+1+-++++-8-+-++++4--

6 Balls, Height 10

(L, Lbound, States) = (188, 188, 210)

Complete: (9 patterns) dual of (4,10) above


6 Balls, Height 11

(L, Lbound, States) = (420, 420, 462)

Complete: (59346 patterns) dual of (5,11) above


7 Balls


7 Balls, Height 8

(L, Lbound, States) = (8, 8, 8)

  88888880

7 Balls, Height 9

(L, Lbound, States) = (32, 32, 36)

Complete: (1 pattern)
  ++++++1+-+++++1++-++++1+++-+++5-

7 Balls, Height 10

(L, Lbound, States) = (108, 108, 120)

Complete: (1 pattern)
  ++++++1+--+++++1++--++++4-+++-+++1+-+++-++1++-+++-+8-++-++++1+-++-+++6-+-+++++1+-+-++++1++-+-+++4-++++-++7--

7 Balls, Height 11

(L, Lbound, States) = (300, 300, 330)

Complete: (144 patterns) dual of (4,11) above


8 Balls


8 Balls, Height 9

(L, Lbound, States) = (9, 9, 9)

  999999990

8 Balls, Height 10

(L, Lbound, States) = (40, 40, 45)

Complete: (1 pattern)
  +++++++1+-++++++1++-+++++1+++-++++1+++6-

8 Balls, Height 11

(L, Lbound, States) = (149, 150, 165)

Type I Incomplete: (18 patterns) dual of (3,11) above

Type II Incomplete: (0 patterns)


8 Balls, Height 12

(L, Lbound, States) = (452, 452, 495)

Complete: (45 patterns) dual of (4,12) above


9 Balls


9 Balls, Height 10

(L, Lbound, States) = (10, 10, 10)

  AAAAAAAAA0

9 Balls, Height 11

(L, Lbound, States) = (50, 50, 55)

Complete: (1 pattern)
  ++++++++1+-+++++++1++-++++++1+++-+++++1++++-++++6-

9 Balls, Height 12

(L, Lbound, States) = (200, 201, 220)

Type I Incomplete: (28 patterns, 3.2 hours) dual of (3,12) above

Type II Incomplete: (2 patterns, 4.8 hours) dual of (3,12) above


9 Balls, Height 13

(L, Lbound, States) = (660, 660, 715)

Complete: (at least 245 patterns -- calculation not completed) dual of (4,13) above