You’re in a pitch-dark room. On a table before you are 12 pennies. You know that 5 are heads up and 7 are tails up, but you don’t know which are which. By moving and flipping the coins you must produce two piles with an equal number of heads in each pile. How can you do this without seeing the coins?I was not able to solve this on my own and had to peek at the answer. Even after seeing the answer, it took me a long time to comprehend why it works.
I'll add some thoughts in the Comments section, but for the answer, go to Futility Closet.
When you create the piles described in the Answer, you will have X heads in the first pile, and 5-X heads in the second. The first pile will also have 5-X tails.
ReplyDeleteAfter you flip all the pennies in the first pile, the 5-X tails become 5-X heads ... same as the second pile.
correct me if I'm wrong.... but the original question does not say that the heads had to be upright, it just says "You must produce two piles with an equal number of heads in each pile" It does not say an equal number of heads have to up. so therefore, just split them into two piles of six. There will be six heads in each group, as well as six tails.
ReplyDeleteArlene
Ah, semantics.
ReplyDeleteThe first part of the puzzle already states that some are heads up, some are showing tails. It could be worded better to make it more obvious that it means you're to end up with pennies that are heads up. Otherwise, the simple way out is to say that all the pennies have heads, regardless of position, and be done with it.