1 entry tagged the wall, newest first.
A hundred people each open half the boxes and every one of them must find their own name. Guessing gives one chance in 2^100. Following the loops gives 31.2%, and the number barely moves as the hundred becomes a million: it settles on 1 minus the natural log of two. The argument works because a cycle longer than half the boxes is the only one of its kind — and this page shows exactly where that stops being true.