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Introduction to Logic

Puzzle - Coins

A man comes back from a business trip with 100 coins to share with his two children. He places the coins on a table with 60 of the coins heads up, and the rest tails up. Then he turns out the light so that it is completely dark. He tells his son that he can do anything he likes with the coins on the table (flip them, rotate them, move them, etc.), but then he must split them into two groups. Then he tells his daughter that she may decide which of the two groups is hers, and which is her brother's. They will then turn the light back on, and each child may only keep the coins in his or her group that are heads up. (Dad gets to keep all the tails up coins.)

When the light is off, the children cannot see the orientation of the coins, and it is impossible to distinguish the orientation by feel alone. The little boy is determined not to let his sister "win" by ending up with more coins than him, so he wants to split up the coins into groups that will *guarantee* that, no matter which group his sister picks, they will both end up with the same number of coins. What should the little boy do?

Puzzle - Coins

A man comes back from a business trip with 100 coins to share with his two children. He places the coins on a table with 60 of the coins heads up, and the rest tails up. Then he turns out the light so that it is completely dark. He tells his son that he can do anything he likes with the coins on the table (flip them, rotate them, move them, etc.), but then he must split them into two groups. Then he tells his daughter that she may decide which of the two groups is hers, and which is her brother's. They will then turn the light back on, and each child may only keep the coins in his or her group that are heads up. (Dad gets to keep all the tails up coins.)

When the light is off, the children cannot see the orientation of the coins, and it is impossible to distinguish the orientation by feel alone. The little boy is determined not to let his sister "win" by ending up with more coins than him, so he wants to split up the coins into groups that will *guarantee* that, no matter which group his sister picks, they will both end up with the same number of coins. What should the little boy do?

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