Table of Pennies, a Blindfold, and Mittons
A table has an unknown quantity of pennies lying on it. Exactly ten of the pennies are heads up and the rest are tails up. You are blindfolded and wearing mittens so that there is NO way that you can determine precisely which pennies are heads up and which are tails up. You may however pick the pennies up, move them around, and flip them over.
Your Task: Explain how you can separate the pennies into two groups so that each group has exactly the same number of pennies with heads up.
Notes: The solution does not in any way involve identifying which specific pennies are heads up vs. tails up. The fundamental assumption is that this is impossible. And no, it does not matter how many pennies in total are on the table—only that initially ten of them are heads and the rest are tails.
Hint: What if the number of tails up pennies is odd? Even? Can you devise a common strategy to handle both cases?
Solution Commentary: Rather than provide a solution, I refer you to the web site where I found this problem. It includes several suggested aolutions. Are they correct from your point of view?