kwc

Coin puzzle

Here's a puzzle to waste your weekend on. Got it from toons.

Professor S.F. Mann has just returned home, surprisingly unscathed, from a lecture in New Haven. He realizes that he has collected 100 Sacagawea dollars in change from the train ticket vending machines. He tells his kids Billy and Mary that he'll split some of the coins with them. He goes in to his dark room alone and places the coins on a table with 60 of them heads-up. S.F. then tells Billy that he must arrange the coins into two piles without the aid of any light. Afterwards Mary will be allowed to choose which pile is hers and which is Billy's. The children will then receive all of the Sacagawea coins that are heads-up in their respective piles, and S.F. will take the remaining coins. Billy hates losing to Mary and so his goal is to divide the coins up so that each pile contains the same number of heads. He is allowed to shuffle and flip the coins whichever way he wants, but he cannot tell which side is heads up while he is putting them into two piles (the room is dark, and Billy's sense of touch is a bit dim too). What should he do?

I'll post an answer next week, but for now I will state the following:
- Billy cannot stand the coins on edge
- Billy cannot walk away with any coins
- The solution for this problem works all of the time (i.e. the solution does not rely on probability over time)