Monday, December 17, 2007

Blind coin-sorting solution

A few days after posing a puzzle to you, I begin to tire of your complaints of hunger. "Oh fine!" I say. "I'll tell you the answer."

Taking your blindfold, I place it around my own head. Your eyes slowly adjust to the light. "Observe!" I say. I divide the pennies into two groups, one of which has five pennies. I flip over every single penny among the group of five. You suddenly realize that each group is showing equal numbers of tails. When I had isolated a group of five pennies, a certain number X of those would be showing tails, and there would be 5-X showing tails in the other group. Once I flip over all the pennies in the group of five, there would be 5-X pennies that were tails-up. Therefore, no matter how I divided it up, there would always end up the same number of tails in each group.

You exclaim,
"I could have figured that out!" I applaud your confidence and offer to show you another "party trick". After a brief pause, you say, "Oh! I've got a call. (It's on vibrate.)" You fumble around and pull out your phone. "Really? I'll be right there!" Closing the phone, you say to me, "Sorry, I've got to go," and then you run off. I smile, and then carefully count my pennies.