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Can you solve it? This TV show is flipping brilliant!

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July 6, 2026 · 1:14 PM
Can you solve it? This TV show is flipping brilliant!

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Alex Bellos's Monday puzzleMathematics

Can you solve it? This TV show is flipping brilliant!

A probability puzzle

Alex Bellos

Mon 6 Jul 2026 02.10 EDT Last modified on Mon 6 Jul 2026 02.59 EDT

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Today’s puzzle imagines a TV game show.

The compere announces that at the end of the show two people will be chosen and each placed in a separate booth.

In the booth, each of them will flip a fair coin, out of sight of the other person but visible to the audience.

Then each of them must guess what the other person flipped – heads or tails. If they both guess correctly, they receive a prize.

The chance of each person guessing correctly is 50 per cent. So the chance of both of them guessing correctly is 25 per cent.

Or is it?

You’re in the studio watching the show, and to your surprise, you and your friend are called up to play the game. As you walk up to the stage, you whisper a strategy to your companion that gives you a better than 25% chance of winning the prize. What is this strategy, and what is the probability of winning?

I’ll be back at 5pm UK with the answers.

PLEASE NO SPOILERS – discuss your favourite game shows. (Real or imaginary.)

Thanks to Henk Tijms for today’s puzzle. Henk is Emeritus Professor of Operations Research at VU Amsterdam and the author of several books on probability.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.

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Alex Bellos's Monday puzzle

Alex Bellos's Monday puzzle

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  • 100suns 43 minutes ago 100suns 43 minutes ago 0 A sub question: find the optimum strategy and prove it is. Reply

    • [100suns](https://profile.theguardian.com/user/id/13299353) [42 minutes ago](https://discussion.theguardian.com/comment-permalink/175088815)   [100suns](https://profile.theguardian.com/user/id/13299353) [100suns](https://www.theguardian.com/science/2026/jul/06/can-you-solve-it-this-tv-show-is-flipping-brilliant#comment-175088787) [42 minutes ago](https://discussion.theguardian.com/comment-permalink/175088815)      0     Also: find the pessimal strategy and prove it is [Reply](https://profile.theguardian.com/signin?returnUrl=https://discussion.theguardian.com/comment-permalink/175088815&componentEventParams=componentType%3Didentityauthentication%26componentId%3Dsignin_to_reply_comment)         

  • [Iforgotmynameagain](https://profile.theguardian.com/user/id/101233022) [1 hour ago](https://discussion.theguardian.com/comment-permalink/175087884)   [Iforgotmynameagain](https://profile.theguardian.com/user/id/101233022) [1 hour ago](https://discussion.theguardian.com/comment-permalink/175087884)      0     I'm guessing we can't pull a Charles Ingram and have someone in the audience cough 1 time for heads and 2 times for tails? [Reply](https://profile.theguardian.com/signin?returnUrl=https://discussion.theguardian.com/comment-permalink/175087884&componentEventParams=componentType%3Didentityauthentication%26componentId%3Dsignin_to_reply_comment)

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