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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