Coins on the table Puzzle
You’re in a completely black room. Scattered on the floor are 100 coins – 90 of these are heads up and 10 of these are tails up. You are unable to distinguish which coins are heads or tails by touch or any other method you can think up like by touching etc.How do you separate the 100 coins into 2 piles, so that both piles contain the same number of face up tails?
The important thing to note here is that the piles can be of different size .Choose any 10 coins to make one pile, then turn over all 10 coins in that pile. The number of tails in this pile is now equal to the number of tails in the other pile of 90 coins. To see this, suppose there were x tails in the 10-coin pile. Since there were initially a total of 10 tails, there must be 10-x tails in the pile of 90 coins. When you flip over all 10 coins in the smaller pile, the x tails in that pile become heads and the remaining coins, which must be 10-x heads, become tails. That matches the larger pile.
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