One Hundred Coins

3.5 stars

You are in a dark room with 100 coins on a table, 12 are heads and the rest are tails, and the two faces are completely indistinguishable in the dark.

How do you separate the coins into two piles so that the number of face up heads in each pile are equal?


Answer: make a pile with 12 random coins and turn them over 

  • Hard
  • Logic
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The answer doesn't make sense, it wouldn't work every time
- Joey (22 Apr 2014)

Can't you just feel the coins?! I mean I personally know the feel difference between a face of heads and a face of tails...
- Katryn (11 Jun 2014)

Clever problem, but not well stated. Last sentence should go something like this: "How do you separate the coins into two UNEQUAL piles so that the PROBABLE number of face-up heads in each pile is equal." If you don't require unequal piles, the solution is to just create two equal piles! The solution is clever: 88 coins with a 12% probability of heads yields, on average, 88 x .12 = 10.56 heads, and 12 coins with an 88% probability of heads yields, on average, 12 x .88 = 10.56 heads.
- Ron (3 Jul 2014)

Contrary to the other comments, this answer works every time and isn't a matter of probability. The subpile of 12 coins will contain X heads coins, where X is between 0 and 12; the bigger pile contains (12-X) heads coins. When you flip the subpile, it goes from having X heads coins to having (12-X), which is of course the same number as the larger pile.
- Andrew (25 Mar 2015)

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