7/24/2016, Rick L. Shepherd

OEIS Sequence A275360:
Maximum number of moves available to one side from a legal chess position with n pieces (with no
additional pieces from promotion).

For completeness:  if a side has two Bishops, those Bishops must be on opposite-colored squares (as in the
original board configuration).

The chess positions below are given in Forsyth-Edwards Notation (FEN). In each position, it is White's move.
These constructed positions support the initial terms and the best lower bounds now known to me for the other
terms and stated in the sequence comments. Parenthetical comments are given, including the number of White
moves and credit to the composers of three of these positions. The other positions exhibit either my simple
examples of many possible for the smallest n, my (sometimes-slight) adaptations, as indicated, of J. Ban's position,
or my own ideas (unavoidably influenced somewhat by all these composers and by the similarities of our tasks).

Any corrections or improvements are welcomed.

Legal chess positions require at least two pieces on the board, the two Kings.

n=2: 8/8/3k4/8/8/3K4/8/8 w - - 0 1 (8 moves)
n=3: 8/8/3k4/8/4Q3/2K5/8/8 w - - 0 1 (35 moves)
n=4: 8/8/3k4/8/4Q3/2K5/5R2/8 w - - 0 1 (49 moves)
n=5: 1R6/8/2K5/8/3Q4/6R1/4k3/8 w - - 0 1 (63 moves)
n=6: 1R6/8/2K1B3/8/3Q4/6R1/4k3/8 w - - 0 1 (74 moves)
n=7: 8/3k4/1R6/4B3/2Q5/5B2/3K4/6R1 w - - 0 1 (85 moves)
n=8: 8/3k4/1R6/4BN2/2Q5/5B2/3K4/6R1 w - - 0 1 (93 moves)
n=9: 8/3k4/1R6/4BN2/2Q5/5B2/3K1N2/6R1 w - - 0 1 (99 moves)
n=10: 8/3k3P/1R6/4BN2/2Q5/5B2/3K1N2/6R1 w - - 0 1 (103 moves)
n=11: 4b3/3P1P2/1K1BN3/7R/4B3/2Q5/R7/3k4 w - - 0 1 (109 moves)
n=12: 4b3/3P1P2/1K1BN3/7R/4B1N1/2Q5/R7/3k4 w - - 0 1 (115 moves)
n=13: 4b1r1/3P1P2/1K1BN3/7R/4B1N1/2Q5/R7/3k4 w - - 0 1 (119 moves)
n=14: 4n1n1/k2P1P1P/1R6/4BN2/2Q5/5B2/3K1N2/6R1 w - - 0 1 (125 moves)
n=15: 2b1n1n1/k2P1P1P/1R6/4BN2/2Q5/5B2/3K1N2/6R1 w - - 0 1 (129 moves)
n=16: 2r1r1b1/1P1P1P1P/1Q6/3NBNK1/R7/8/4B1k1/2R5 w - - 0 1 (133 moves, after J. Ban)
n=17: n1r1r1b1/1P1P1P1P/1Q6/3NBNK1/R7/8/4B1k1/2R5 w - - 0 1 (137 moves, after J. Ban)
n=18: n1r1r1b1/1P1P1P1P/1Q6/3NBNK1/R7/8/3PB1k1/2R5 w - - 0 1 (139 moves, after J. Ban)
n=19: n1r1r1b1/1P1P1P1P/1Q6/3NBNK1/R7/8/3PB1kP/2R5 w - - 0 1 (140 moves, after J. Ban)
n=20: n1r1r1b1/1P1P1P1P/1Q6/3NBNK1/R7/6p1/3PB1kP/2R5 w - - 0 1 (141 moves, after J. Ban)
n=21: 1n1qr1n1/P1P2P1P/2BN1B1k/2N5/6Q1/4R3/P1PP1K1P/1R6 w - - 0 1 (143 moves, H. F. L. Meyer, 1880;
         note that all White pieces are on the board)
n=22: n1r1r1b1/1P1P1P1P/1Q6/3NBNK1/R7/4p1p1/3PBPkP/2R5 w - - 0 1 (144 moves, J. Ban, 1960)
n=23: n1r1r1b1/1P1P1P1P/1Q6/3NBNK1/R7/4p1p1/3PBPkP/b1R5 w - - 0 1 (144 moves, after J. Ban)
n=24: n1r1r1b1/1P1P1P1P/1Q6/3NBNK1/R7/4p1p1/3PBPkP/b1R4q w - - 0 1 (144 moves, after J. Ban)
n=25: n1n1r1b1/1P1PrP1P/1Q6/3NBNK1/R7/4p1p1/3PBPkP/b1R4q w - - 0 1 (144 moves, after J. Ban)
n=26: n1n1r1b1/1P1PrP1P/1Q6/3NBNK1/R7/4p1p1/p2PBPkP/b1R4q w - - 0 1 (143 moves, after J. Ban)
n=27: n1n1r1b1/1P1PrP1P/1Q6/3NBNK1/R7/p3p1p1/p2PBPkP/b1R4q w - - 0 1 (142 moves, after J. Ban)
n=28: n1n1r1b1/1PpPrP1P/1Q6/3NBNK1/R7/p3p1p1/p2PBPkP/b1R4q w - - 0 1 (139 moves, after J. Ban)
n=29: 1n1b1r1r/K1PpPpPp/pp1N1B1k/2NB3b/6Q1/4R3/P1PP1P1P/qR5n w - - 0 1 (128 moves)
n=30: 1n1b1r1r/K1PpPp1p/pp1N1B1k/2NB3b/6Q1/4R1p1/P1PP1PPP/qR5n w - - 0 1 (117 moves)
n=31: rnbb1r1n/ppppPp1p/1P1N1B1K/k1NB4/6Q1/4R1p1/P1PP1PPP/qR6 w -- 0 1 (105 moves)
n=32: q2Q3r/n6R/kpB1N1K1/p1p1Bppp/1PN3P1/1n1pp1b1/P1PPPP1P/r5Rb w - - 0 1 (99 moves, H. H. Cross, 1946)