The Three Prisoners Puzzle: How To Really Solve It?

Even experts have failed to solve this puzzle correctly!

Hemanth
Street Science

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The Three Prisoners Problem: How To Really Solve It? — An illustration/cartoon showing a warden wearing sunglasses and smirking on the left. On the right, are three puzzled prisoners: A, B, and C. A is wearing a smile on his face, B is wearing a poker face, whereas C is plain surprised. Between the warden and the prisoners is a hanging rope. Who will be hung using this rope?
The warden and the three prisoners — Illustrative art created by the author

The three prisoners puzzle is a fun and engaging mathematical puzzle that shows how counterintuitive the notion of probability can be. I love and work with mathematics day in and day out.

Of all the sub-fields mathematics offers, I feel that probability theory is the one that is the most demanding and rewarding at the same time.

Before we proceed with this puzzle, be warned that it appears deceptively simple and easy on the surface. However, this puzzle has historically even caught out experts in the field of probability. So, bring your best brains with you to solve this one. Let us begin.

The Three Prisoners and the Warden

Our story begins with three prisoners: Arun, Ben, and Cayleb (A, B, and C for short throughout the rest of the puzzle). All three prisoners were sentenced to death a while back.

However, the Governor in charge started coming increasingly under pressure to reduce the death sentence count for the state. So, he came up with a very unfair but convenient plan: the city would pardon random prisoners who were sentenced to death.

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