You are blindfolded, and there are a number of shiny, smooth coins in front of you. One side is purple and the other side is green. Your friend tells you, once, the number of purple coins there are. Your job is to separate the coins so that there are the same number of purple coins on both sides. You can flip any coin as many times as you like. How do you accomplish this, and how do you know when you are finished?

You cannot see through the blindfold, and you cannot tell if a coin is purple side up or green side up.

Assume that you are not allowed to do things like remove your blindfold.

(from the Williams College Math Camp 2017; note that I do not know the actual answer, but if it makes sense to me and the community then I will mark it as the answer)

  • $\begingroup$ The wording of this question is confusing, because it uses "sides" to mean both "faces" (of the coin) and "ends" (of the table you are sitting at). I had to visit the linked duplicate to understand what was being asked here. $\endgroup$ – shoover Feb 4 '18 at 23:10

Oh wow. Turns out you won’t even need to count the green coins. Instead you should just

Separate all the purple coins, and flip them. If you got it right, all coins are now showing green.

This works, because

If you missed, and actually picked some green coins, then for each miss, you get one more purple coin on both sides.

Very nice puzzle, thank you!

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  • $\begingroup$ Could you explain this answer in more depth? Maybe give an example so I can understand it better, because I don't exactly follow. $\endgroup$ – Terry Yu Feb 4 '18 at 7:45
  • $\begingroup$ @TerryYu if there are 7000002 coins, and two of them are purple, your friend will tell you ”two”. You pick two coins and flip them. If you got the two purple ones, the result has zero purple coins on both sides. If you got one purple and one green, then the other purple one is among the seven million, and the green one you picked in its stead gets flipped into a purple one, so both sides have 1 purple coin. If you picked 2 green coins, as is likely, there will be two purple coins on each side. $\endgroup$ – Bass Feb 4 '18 at 8:08

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