The YouTube video The Riddle That Seems Impossible Even If You Know The Answer describes an interesting mathematical problem as well as its solution. Briefly, the problem is as follows:

In a prison, there are 100 prisoners labelled from 1 to 100. In a room within the prison, there are 100 boxes labelled from 1 to 100 on the outside. Inside each box is also labelled from 1 to 100, with the number inside the box being generally unrelated to the number outside the box. All the prisoners go into the room one at a time to try to identify the box containing their own number on the inside. Each prisoner is allowed to look in no more than 50 boxes. If every prisoner finds his own number, then all the prisoners will be freed. But if any prisoner fails to find his own number, then all the prisoners will be executed. Each prisoner must leave the room in the same state as it was before he entered the room. None of the prisoners can observe another prisoner’s search. Nor is any prisoner allowed to communicate with any of the other prisoners after he has completed his search. However, before any of the prisoners search, all of the prisoners are allowed to gather to formulate a search strategy. What should this search strategy be?

KJW said:

The YouTube video The Riddle That Seems Impossible Even If You Know The Answer describes an interesting mathematical problem as well as its solution. Briefly, the problem is as follows:

In a prison, there are 100 prisoners labelled from 1 to 100. In a room within the prison, there are 100 boxes labelled from 1 to 100 on the outside. Inside each box is also labelled from 1 to 100, with the number inside the box being generally unrelated to the number outside the box. All the prisoners go into the room one at a time to try to identify the box containing their own number on the inside. Each prisoner is allowed to look in no more than 50 boxes. If every prisoner finds his own number, then all the prisoners will be freed. But if any prisoner fails to find his own number, then all the prisoners will be executed. Each prisoner must leave the room in the same state as it was before he entered the room. None of the prisoners can observe another prisoner’s search. Nor is any prisoner allowed to communicate with any of the other prisoners after he has completed his search. However, before any of the prisoners search, all of the prisoners are allowed to gather to formulate a search strategy. What should this search strategy be?

Kill the guards and escape.

> What should this search strategy be?

I’ll give it some thought.

Kind of a … weird one because they are like it is supposed to be amazing that you can improve your odds to about 30% whereas that seems unremarkable, basically what I’d expect, just by winnowing down the possibilities

Maybe it’s understood that as each prisoner enters and finds a particular number they re arrange the boxes into above 50 or below 50

You work out a strategy where each successive prisoner sorts the boxes, if you are prisoner 17 you head toward the boxes below 50 ( say on the left hand side) as each prisoner enters they further sort into high side of below 50 and low side of 50 ??

Or cheat

or read the transcript

or read the transcript

twice

I did watch the video. Sounded convincing, but I am still not convinced you will always end up in the correct loop on your opening move.

party_pants said:

I am still not convinced you will always end up in the correct loop on your opening move.

um

every sequence has to end up looping back to its start at some stage

KJW said:

The YouTube video The Riddle That Seems Impossible Even If You Know The Answer describes an interesting mathematical problem as well as its solution. Briefly, the problem is as follows:

In a prison, there are 100 prisoners labelled from 1 to 100. In a room within the prison, there are 100 boxes labelled from 1 to 100 on the outside. Inside each box is also labelled from 1 to 100, with the number inside the box being generally unrelated to the number outside the box. All the prisoners go into the room one at a time to try to identify the box containing their own number on the inside. Each prisoner is allowed to look in no more than 50 boxes. If every prisoner finds his own number, then all the prisoners will be freed. But if any prisoner fails to find his own number, then all the prisoners will be executed. Each prisoner must leave the room in the same state as it was before he entered the room. None of the prisoners can observe another prisoner’s search. Nor is any prisoner allowed to communicate with any of the other prisoners after he has completed his search. However, before any of the prisoners search, all of the prisoners are allowed to gather to formulate a search strategy. What should this search strategy be?

the first one has to get theirs correct or they will all be executed… so they have a 50/50 chance…

dv said:

Kind of a … weird one because they are like it is supposed to be amazing that you can improve your odds to about 30% whereas that seems unremarkable, basically what I’d expect, just by winnowing down the possibilities

Now watched it (first 7 minutes anyway).

It seems pretty unintuitive to me.

I still don’t see why picking a sequence defined by the numbers in the box is way, way better than just picking boxes at random.

I’m off to see if it works.