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1. Shortest stalemate game

2. Double stalemate with 30 men kings left on other cells. No one has found a 17-move game leaving the kings on their own starting squares. The two-king ending is rare among task problems in that 17 moves (by each player) can be proved an absolute minimum. Fifteen captures must be made by each side, but neither player can capture on his first move, and one more noncapture move can be proved necessary.

Dudeney later found a 17-move game (Problem 352 of his Amusements in Mathematics) that eliminates only the 14 pieces (nonpawns) of both sides, leaving both kings and the 16 pawns on their starting cells. Curiously, every move by Black is a mirror copy of White's preceding move. Here again, 17 moves can be proved minimal.

Along similar lines, one of Dudeney's great achievements was a 16-move game ending with all 16 of White's men on their starting cells and Black with only his king on the board. After Dudeney published this game [see Figure 116, No. 3] Loyd discovered that White could checkmate in three moves. This is another minimum, since no shorter mate is believed possible with Black's lone king on any other cell. Can the reader work out the mate before it is revealed in the Answer Section? Dudeney's game (Problem 351 of his Amusements in Mathematics) was reduced by a half-move in 1898—that is, the final position is achieved after White's 16th move—but then there is no mate in three because it is Black's turn.

A special class of task problem is known as a "one-move construction task" because only immediately possible moves are

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