There are 100 coins scattered in a dark room. 90 have heads facing up and 10 are facing tails up. You cannot tell which coins are which. How do you sort the coins into two piles that contain the same number of tails up coins?

Ok, so the way is

if n coins are tails and you want to seperate the big pile into 2 piles with equal number of tails, then you take n coins out of the main pile and flip them all over

explanation

ok, so let's use the xample

you have 10 tails up

let's say x+y=10

you take out 10 random coins

there are x tails and y heads in that pile because x+y=10

since you took out x tails from the main pile, ther are now 10-x or y tails in the main pile

but you have no way of finding those coins

if yo go to the 10 random coinsn yo got, you have y heads but you need y tails

solution? flip all coins in the 10 pile over to get x heads and y tails

The piles aren't and dont need to be the same size, make a pile of ten coins and a pile of ninety coins, flip all of the ten coins and youhave the same number of tails.