Splitting blind coins into piles with equal heads

Question

A thousand coins lie on the floor: exactly $20$ show heads and the other $980$ show tails. You cannot see or feel which side is up, but you may turn over any coins you like. How can you divide the coins into two groups that are guaranteed to contain the same number of heads?

Short answer

Yes: take any 20 coins as one pile and flip every coin in it. If that pile held $m$ heads, the remaining pile holds $20-m$ heads; after flipping, the small pile has $20-m$ heads too, so the counts always match.

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Lessons behind this question

Sample Spaces, Events, and the Probability Axioms
Conditional Probability, Total Probability, and Bayes' Rule

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