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Problem13. Given a rectangular parallelepiped of dimensions (a) $4\times4\times4$; (b) $4\times4\times3$; (c) $4\times3\times3$, consisting of unit cubes. Players take turns skewering a row of cubes (parallel to the edges of the figure), as long as there is at least one cube which is not jet in the row. The player who cannot do so loses.
Problem14. This game begins with the number 2. In one turn, a player can add to the current number any natural number smaller than it. The player who reaches 1000 wins.


Math Circle
1999-08-26