A puzzle from This Week’s Finds, Week 250:

You and your friend each flip a fair coin and then look at it. You can’t look at your friend’s coin; they can’t look at yours. You can’t exchange any information. Each of you must guess whether the other person’s coin lands heads up or tails up. Your goal, as a team, is to maximize the chance that you’re both correct.

What’s the best you can do? If you pick an answer at random, you’ll get it right 1/4 of the time; can you prove that that’s the best you can do? If not, can you find something better?

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