pow:problem3f24
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| pow:problem3f24 [2024/10/08 00:55] – created mazur | pow:problem3f24 [2024/10/10 19:15] (current) – mazur | ||
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| + | <box 85% round orange|Problem 3 (suggested by Prof. Alexander Borisov), due on Monday, October 7. > | ||
| + | Three players are playing a game. They are | ||
| + | taking turns placing kings on a 1000x1000 chessboard, so that the | ||
| + | newly-placed king is not adjacent (directly or diagonally) to any of the | ||
| + | previously placed kings (i.e. the kings are in non-attacking positions). Whoever cannot place a king, loses. Prove that if any two of the players cooperate, they can make the third player lose. | ||
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| + | </ | ||
| + | This problem was created by Prof. Alexander Borisov. We have not received any solutions. For a slightly | ||
| + | edited version of the solution provided by Alexander, see the following link {{: | ||