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Finding Head


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I posted a question similar to this one sometime ago but I thought it fun to revisit and make it a little more challenging, so here we go:

You are wearing a blindfold and thick gloves. An infinite number of quarters are laid out before you on a table of infinite area. Someone tells you that 20 of these quarters are tails and the rest are heads. He says that if you can split the quarters into 2 piles where the number of tails quarters is the same in both piles, then you win all of the quarters. You are allowed to move the quarters and to flip them over, but you can never tell what state a quarter is currently in (the blindfold prevents you from seeing, and the gloves prevent you from feeling which side is heads or tails). How do you partition the quarters so that you can win them all?

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... take 20 quarters and flip them over.



If I took all heads, then after flipping them, I had 20 tails in the pile of 20 and 20 tails in the "infinite" pile.

If I took for example 12 heads and 8 tails, then there was 12 tails left in the "infinite" pile and after flipping the 20 quarters I took, I had 12 tails in the small pile too.
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