The Riddle That Seems Impossible Even If You Know The Answer

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When you factor in the odds of one nerd convincing 99 other convicts to go with this strategy, your chances quickly fall back to zero.

As somebody that's tried tracking down a CD left in the wrong CD case, I can attest that the loop strategy does indeed work 31% of the time. (The other 69% of the time it turns up weeks later on the kitchen table.)

really sad that these prisoners were so good at math and cooperation, yet still ended up in jail 😢

A really incredible feature of the loop strategy is comparing how well it works even against random guessing with more chances to open boxes. For example, if each prisoner were allowed to open 99 of the 100 boxes, instead of 50, to find their own number, the total probability of success by randomly guessing is only 0.99^100, or 36.6%! (Whereas the loop strategy gives a comparable chance of success while only opening 50 boxes, and succeeds 99% of the time if you can open 99 boxes) If you were allowed to open 98 of 100 boxes, the chance of winning via random guessing drops to 13.3%, and to below 5% for 97 boxes!

I think the chance of convincing 99 other prisoners that this strategy is their best chance of survival is much lower than 31%.

Memorizing this just in case I'm ever trapped in a prison with a sadistic mathematical prison warden

I was really confused at first on how whatever number you start with is guaranteed to be in your loop, but once I started to type out a comment questioning it I totally realized how it works. In order to finish your loop you have to end up back where you start, and since none of the boxes can be empty, you're guaranteed to be in some sort of loop.

The main point here is that "failing hard" comes with no harsher penalty than "failing little"....hence, you can redistribute your loss function to take advantage of this. Great video, btw!

Interesting corollary: If prisoner #1 (or any other prisoner) finds that his own loop has a length of exactly 50, he immediately knows there's a 100% chance of success.

Imagine being the first inmate and not finding your number. “Oof, we tried”

When you first gave the solution, I sketched out on a piece of paper a version of the problem with 4 prisoners, 4 boxes, 2 attempts, and I feel like I understood the entire thing almost instantly with no further explanation required. I think lowering the numbers down to something more manageable makes the problem much more comprehensible. I mean, you could even write out 4! configurations if you wanted and prove that it works for all of them, whereas 100! is so large as to be impossible to visualize.

So, I think there’s an easier explanation for why you’re guaranteed to eventually circle back to your own box.

My actual concern if this ever somehow became a situation I got myself into is that someone would decide this is stupid and just pick boxes at random

If you think the riddle is hard, imagine trying to convince 99 fellow prisoners to follow the plan to the letter.

I feel like there needs to be a 'wow out loud' like 'laugh out loud', because when you said "that's like scaling up a millimetre to the diameter of the observable universe", that's exactly what I did.

I've seen a variation of this some years ago. Didn't remember the way to solve but it came back quickly when you gave the solution.

6:35

As someone that went to prison, I can tell you with 100% confidence, that they got more chances to win by randomly picking boxes (one in 8*1^32), than 100 of them to agree to ANY strategy.

Love this! The concept of loops does break the mind slightly, but is very logical once you look at it with a reduced number of boxes. I would never come up with this solution myself, however - eliminating randomness of prisoners' choices in this manner is truly ingenious.