[math-fun] othello puzzles...
As a lower bound, this real (as opposed to artificial) othello game, a 64-0 wipeout by white (who makes lowercase moves), involves 23 passes by black (uppercase moves): F5d6C4g5D7c7H5d8B8b7B6a7b5A6a5b4B3c6E8f8C8a8e7a4b2A2c2D2d1e2F2c5c3a1a3e6d3f6F7f1g2H2e3F4b1g1c1e1g8g7f3h1h3h4h6 count of passes so far: 1 2 3 4 5 6 7 8 9 a b c d e f 0 1 2 3 4 5 6 7 assuming I did not screw up. The maximum possible number of passes is clearly <=61 since two consecutive passes end the game (by rules). And if one cannot pass during first 10 moves, upper bound shrinks to 51. Concerning the question of the shortest possible non-wipeout game, here's an 11-move nonwipeout game (15 disk final position): 1.f5 2.f4 3.c3 4.e6 5.f7 6.g6 7.g4 8.e8 9.g8 10.g5 11.h5 ends B14, W1: ........ ........ ..B..... ...BBBB. ...BBBBB ....B.B. .....B.. ....W.B. Re the max-mobility question: I found a position with mobility=25 arising in a real game, but it is certainly increasable. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)
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Warren D Smith