The Prisoner Box Riddle

Ten band members, ten boxes, and each musician can only open five to find their instrument. Is there a strategy to help the hapless combo find all of their own instruments? Apparently so, according to this puzzle from TED-Ed.

(YouTube link)

They explain why this is supposed to work, but I can’t really wrap my head around why the strategy gives them any better odds than randomly opening boxes would. Maybe it’s just too late at night for me to see it. -via Viral Viral Videos

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Vastly better explanation of the strategy here:

"The magic of this solution ISN'T that it gives better odds for any single individual to find their [instrument], because it doesn't [still 50/50]. It's that all the successes or failures are forced to happen together. Everyone wins together [30% of the time], or everyone loses together [70% of the time]. Your fates are linked..."

Think of it this way... Just by random chance, each instrument COULD end up in its correct box. Or they could all end-up one-step removed, two steps removed, etc. Then EVERYONE would only have to try one/two/three boxes, and they would ALL (not just one or a few of them) succeed. If instead they tried opening boxes in a random order, somebody in the group would invariable need to try all 10 boxes before getting it right, and you'd never stand a chance of everyone winning.
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