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Название: Mathematical games
Авторы: Lukacs C., Tarjan E.
Players take turns to remove any number of objects from one of n rows. The player who takes the last object wins.
Ans:If a game is played with a finite set of numbers and each move changes only one set and the game terminates, it is equivalent to NIM.
To determine who should win, write the sizes of the piles in binary. Add the columns (no carrying). If the sum of each column is even, the person to play loses. (from Mathematical Carnival)
In the reverse game the player who takes the last counter loses
Ans: The strategy in the reverse game follows the normal game until only one row has more than one counter. Then you take away either all the biggest row or all but one of this row so as to leave an odd number of rows.