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Coin Flipping Puzzle: Interview Question

Golu has 100 identical coins (with head side and tail side) which he wants to donate to someone. There are many people who are aiming to get this collection of 100 coins. So Golu created a puzzle using all 100 coins and declared that the one who will solve his puzzle will get all the coins. You desperately need money so solving the puzzle is only option you have.

The Problem goes like this:
All 100 coins are laying flat on a table. 80 of them are heads up and remaining 20 are tails up. You can’t feel, see or in any other way find out which side is up. Split the coins into two piles(sets) such that there are the same number of tails in each pile.
[Baby Hint]: If number of coins in first pile is n then other pile will have 100-n coins.



First try yourself before peeking into the solution below. 


Solution:

Solution is very easy. Divide the pile of 100 coins into two separate piles of 80 and 20 coins respectively. Just flip every coin of the pile of 20 coins and you will have same number of tails up(also same number of heads) in both piles.

Too easy to digest, huh. Let’s see mathematically what’s happening. You have just divided 100 coins into two piles of 20 and 80 coins each. Since you can’t see so you have no idea how many tails/heads up are there in two piles. Let’s assume that the number of tails up in first pile(20 coins pile) is X then number of heads up coins would be 20 - X. Since, initially total number of tails up coins was 20 so number of tails up coins in second pile(80 coins pile) would be 20 - X. If you flip every coin of first pile then all X tails up coins will become heads up and remaining 20 - X heads up coins will be now tails up. Second pile is already having 20 - X tails up coins so we have now equal number of tails up coins in both piles. And since they have equal number of tails up coins means they also have same number of heads up coins. Easy right!!
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