Why can following a loop make everyone more likely to succeed?
Six people each need to find their own number in six closed boxes, but each may open only three. If everyone must succeed, following the number found in each box creates a very different game from making independent guesses.
Questions you could explore
- What makes a long loop dangerous to the whole group?
Start reading
- Uri Mendlovic / arXivThe Prisoners and the Swap: Less than Half is Enough
Section 1.1 explains the standard numbered-box strategy and why success depends on the longest cycle. The later single-swap variant is a separate problem.
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