I watched the video, and was very confused. Turns out the solution is right, but his explanation was - mildly phrased - flawed, when calculating the probability of cycles ("loops") of length N to N/2+1.

I had to reconstruct the correct solution.

But that's YouTube nowadays, trimmed to maximum emotional show effect for the sake of clicks

FWIW: if you still struggle to understand the solution, try the case N=4. There are only 24 = 4! possible configurations of the boxes, this easily fits on a piece of paper.

And you can see why there are exactly N!/C configurations with a cycle length C, for N >= C > N/2. In the case of N=4 there are

Hence the survival rate is at 10/24.

Cheers Rolf
(addicted to the Perl Programming Language :)
see Wikisyntax for the Monastery

†) updated

In reply to Re^2: Proving Veritasiums riddle using Perl (simulating "100 prisoners problem") by LanX
in thread Proving Veritasiums riddle using Perl by cavac

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