Monday, March 29, 2010

Kings and Queens and Counting Coins

I found this one at Nick Yees Homepage.

In Rengefall, copper coins are minted with the portrait of the Queen on one side and the portrait of the King on the other side.

On this day, the half-crazed executioner gives the captured Talin one chance to avoid execution. The executioner brings Talin into an unlit room. He tells Talin that scattered on the table in front of him are one hundred copper coins of which twenty have the Queen side facing up while the rest have the King side facing up. If Talin can separate the coins into two piles, each with the same number of Queens facing up, he will release Talin. One other constraint is that Talin must accomplish this task in 5 minutes. If Talin fails, he will be beheaded.

It is impossible for Talin to see which side the coins are facing up in the darkness, and the contours of the portraits are too similar to decipher by touch. Nevertheless, Talin managed to separate the coins into two piles with the same number of Queens facing up in the time allotted. How did he accomplish this?


  1. He turned all the coins on to their sides - one coin every 3 seconds may be a little quick, but if your life depended on it daresay it could be done!!

  2. I would have certainly tried!

    But I think there is another solution.

    Create two piles of 20 and 80 coins. Then take the pile of 20 coins and flip them over. You will now have the same number of heads in each pile.

    Explanation: If the pile of 20 coins had x heads in it (before you flip them), then the pile of 80 coins had 20-x heads. The pile of 20 had 20-x tails.

    Flip the pile of 20 coins over, and you now have 20-x heads, the same as what is in the pile of 80 coins.


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