mathematics - Variation of 100 Gold Coins Puzzle - Puzzling Stack Exchange

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• cards in darkness 5 answers

you blindfolded (and can’t see thing). there $100$ coins lying on table. of these coins, $80$ tails-up , $20$ heads-up. need divide them 2 groups of $x$ , $y$ each (with $x+y = 100$). can pick coin , flip (if tails, become head , if head, become tail), can't see don't know coin flipping. in end, both groups should contain equal number of heads.

the trick simple: when dividing, make first pile big number of heads-up coins, i.e. 20. first pile contains unkown number of heads-up coins, call number n. second pile of 80 coins contains remaining 20-n heads-up coins. flip coins in first pile , both piles contain 20-n heads-up coins, regardless of value of n.