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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)

Comments (5)

bp:

I'm no good at these puzzles anymore, but I think the answer is:

He should just flip each coin once, and put half of the coins in one pile and half in the other. Since coin flips are independent events, each pile should have roughly 25 heads in it. There's certainly no way for him to know which pile has more, and the expected value of number of heads for each pile is 25.

Am I right, or just horribly, horribly wrong? :)

Rakesh:

Hi, I has thought exactly like the one in the previous comment but I am very anxious to know the answer. Please help me.

daman:

Should I post the answer? I already figured this out...

The solution is confusing as the problem. I think he should just give the kids all the Sacagewea coins and buy silver coins instead.

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This page contains a single entry from kwc blog posted on July 9, 2004 6:29 PM.

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