Three Prisoners with Skullcaps — An Alternative Solution

Itai Zukerman posted an interesting solution to the Three Prisoners with Skullcaps puzzle (in response to Gerrymandering Probability — the post with the solution). Apparently comments don’t support tables, so I’m posting a response here with a table laying it out:

Groucho Chico Harpo Action Outcome
White White White Groucho guesses White, others pass Win
White White Black Chico guesses White, others pass Win
White Black White Harpo guesses White, others pass Win
White Black Black Groucho guesses Black,
Chico guesses White,
Harpo guesses White
Lose
Black White White Groucho guesses White,
Chico guesses Black,
Harpo guesses Black
Lose
Black White Black Harpo guesses Black, others pass Win
Black Black White Chico guesses Black, others pass Win
Black Black Black Groucho guesses Black, others pass Win

So the outcome is the same as the solution I proposed: there are six correct guesses “cracked” among six scenarios for six wins overall, and six incorrect guesses “packed” into two scenarios for two losses overall.

I wonder how many other ways the prisoners can plan to accomplish the same thing.

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