Home > Riddles > The 100 coins a ciegas
The scene seems doomed to trial and error: you know how many coins are face up, but you can't recognize any of them. The charm of the problem is that the solution does not need to see better, but rather to cut with precision.
There are 100 coins on a table. You know that exactly 20 are facing up and 80 are facing down, but you are completely in the dark and cannot distinguish one from the other by touch.
You can separate coins into two piles as you like and also turn over the coins as you need. Can you make two piles so that they both have the same number of coins face up?
Answer: Separate any 20 coins into one pile, leave the other 80 in the other pile, and turn over the 20 from the first pile. Let x be the number of initial faces in that pile of 20. Then in the pile of 80 there are 20-x faces (because the total number of faces is 20). When turning the 20 coins, the x heads become tails and the 20-x tails become heads; Therefore the pile of 20 is left with 20-x faces. The pile of 80 already had 20-x faces. Result: both piles end up with the same number of heads.
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