Introduction to Logic ToolsforThought

 Coiins

 A logic professor 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 rearrange the coins on the table (move them, flip them, etc.) but in the end there must be 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 keep only 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, she will not end up with more coins than he does. What should the little boy do?