next up previous
Next: More problems Up: Games Previous: Analysis from the endgame

Homework problems

Problem10. Ten 1's and ten 2's are written on a blackboard. In one turn a player may only erase any two figures. If the two figures erased are identical, they are replaced with a 2, if they are different, they are replaced with a 1. The first player wins if a 1 is left at the end and the second player wins if a 2 is left.
Problem11. The number 60 is written on a blackboard. Players take turns subtracting from the number on the black board any of its divisors and replacing the original number with the result of the subtraction. The player, who writes the number 0 looses.
Problem12. A knight is placed on square a1 of a chessboard. Players alternate moving the knight either two squares to the right and one square up or down, or two squares up and one square right or left (the usual knight moves but in restricted directions). The player who cannot move loses.


Math Circle
1999-08-26