You have 10 coins on a table: 5 heads and 5 tails. You are blindfolded, and can touch the coins but have no way of finding out which ones are head and which ones are tails. You can flip any of the coins over, or toss them however many times you want. Here’s the question: How can you make two piles of 5 coins which each have the same number of heads? Try out the question yourself, and when you want to see the answer, scroll below the picture.
It seems quite unintuitive, right? You can’t tell heads and tails apart, and so what can you do? Let’s see: if you split the 10 coins into 5 and 5, one set will have n heads and the other will have 5-n heads. So that second set will have 5-(5-n) tails, which is n tails. So if you flip all the coins in the second set, all the tails will become heads and heads become tails. This reverses it, so now there are 5-n tails and n heads. Both sets have equal heads! I have to say, this answer makes me feel quite dumb, considering upon reading the question I almost disregarded it as impossible.