Question

Sonia and Roberto are playing. They play alternately removing 1, 2, 3, 4 or 5 tiles from a stack. Whoever takes the last tile or tiles loses. At one point in the game, there are ten tiles left in the pile and it is Sonia's turn to remove some tiles. The number of chips that Sonia must leave Roberto to be sure that she will win is:

Answer 1

i want to say A, 9.

Explanation:

The answer is (A) 9.

If Sonia removes 1 tile from the pile of 10 tiles, there will be 9 tiles left.If Roberto removes 1 tile, then there will be 8 tiles left. Sonia can remove 2 tiles, leaving 6 tiles for Roberto.

If Roberto removes 1, 2, or 3 tiles, then there will be 5, 4, or 3 tiles left, respectively. Sonia can then remove enough tiles to leave Roberto with a multiple of 6 tiles, ensuring a win on her next turn.For example, if Roberto removes 3 tiles, then there will be 7 tiles left. Sonia can remove 2 tiles, leaving 5 tiles for Roberto. Then, regardless of how many tiles Roberto removes, Sonia can always remove enough tiles to leave Roberto with a multiple of 6 tiles on his turn, ensuring a win on her next turn.