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Revision as of 11:36, 14 July 2014

This article contains a translation of Problem der 100 Gefangenen from de.wikipedia.

A fact from 100 prisoners problem appeared on Misplaced Pages's Main Page in the Did you know column on 14 July 2014 (check views). The text of the entry was as follows: Did you know... that two incommunicado game show contestants can use the 100 prisoners problem to maximize the odds of sticking Monty Hall with the goat? A record of the entry may be seen at Misplaced Pages:Recent additions/2014/July. The nomination discussion and review may be seen at Template:Did you know nominations/100 prisoners problem.

Creation request

The following request was added some time ago to Misplaced Pages:Requested articles/Mathematics#Recreational mathematics, which I have now moved here:

• The condemned prisoners and the boxes Fun problem with surprisingly simple solution. See for example http://www.mast.queensu.ca/~peter/inprocess/prisoners.pdf

This source might be added to the article if it adds anything. Frieda Beamy (talk) 17:52, 30 June 2014 (UTC)

Thanks for the notice, but the article has better sources. Best wishes, --Quartl (talk) 18:07, 30 June 2014 (UTC)

Example

The first example is as follows:

The prison director has distributed the prisoners' numbers into the drawers in the following fashion

number of drawer	1	2	3	4	5	6	7	8
number of prisoner	7	4	6	8	1	3	5	2

The prisoners now act as follows:

• Prisoner 1 first opens drawer 1 and finds number 7. Then he opens drawer 7 and finds number 5. Then he opens drawer 5 where he finds his own number and is successful.
• Prisoner 2 opens drawers 2, 4, and 8 in this order. In the last drawer he finds his own number 2.
• Prisoner 3 opens drawers 3 and 6, where he finds his own number.
• Prisoner 4 opens drawers 4, 8, and 2 where he finds his own number. Actually, this was already known to prisoner 1.
• That prisoners 5 to 8 will also find their numbers can also be derived from the information gained by the first three prisoners.

Unless I'm missing something, Prisoner 4 is a maverick, Prisoner 1 is psychic, and Prisoner 2 is forgetful:

1)"Prisoner 4 opens drawer 4, 8 and then 2." Prisoner 2 has already indicated that number 4 is in drawer 2 so Prisoner 4 could have just opened that directly. Why does Prisoner 4 open two more drawers? Drawer 4 we already know contains the number 8 and drawer 8 is already open/empty/out of the game as Prisoner 2 found their number in it. If all the combinations were not known there would be an advantage to not going directly to your number, as opening your allotment (not the allotment - 1 as Prisoner 4 does here) would provide more information for the subsequent prisoners, but in this case all the drawer/number combinations have already been identified. Poor Prisoner 4.

2)"Actually, this was already known to prisoner 1." Prisoner 1 opened drawers 1,7, and 5 so how would they have known that drawer 2 contained number 4? "Prisoner 2 opens drawers 2, 4, and 8 in this order." So it was Prisoner 2 not Prisoner 1 that knew drawer 2 contained number 4.

I am as mathematical as I am musical (Lalahalah-sqreeKK-La), so I'm quite prepared to be told I haven't understood, but in that case the examples could do with fleshing out. Belle (talk) 08:05, 1 July 2014 (UTC)

The prisoners are not allowed to communicate with each other. Maybe the phrase "was already known" is misleading, I'll reformulate it. Best wishes, --Quartl (talk) 08:11, 1 July 2014 (UTC)

Sorry, it seems I mixed up prisoners 1 and 2. Thanks for pointing this out. --Quartl (talk) 08:16, 1 July 2014 (UTC)

Ahhhhhhh, I see. I thought the prisoners were observing the previous attempts...You should probably remove "Actually, this could have been derived from the information gained by prisoner 2", because the prisoners could not have derived it and the observer can only derive it by altering the parameters of the problem. It's confusing for mathematical dummies like me and probably not helpful for maths types. Belle (talk) 08:31, 1 July 2014 (UTC)

At this point, a change of perspective from the prisoners' view to an outsider's view is made. Actually, this change of perspective is intentional, since we don't want to carry out the same computations again and again. Do you think it would be more instructive to state all opened drawers for all prisoners first and afterwards argue that an outside observer would have known that the prisoners will survive already after the third one? Best wishes, --Quartl (talk) 08:49, 1 July 2014 (UTC)

I made the change of perspective clearer in the article. --Quartl (talk) 09:17, 1 July 2014 (UTC)

Yes, that's better. (Now I've re-read it, it is clear that the remaining prisoners do not see the previous attempts. It was early, I hadn't had coffee. Excuses, excuses). Belle (talk) 09:24, 1 July 2014 (UTC)

Don't worry, your remarks were certainly helpful. It is a difficult subject. Best wishes, --Quartl (talk) 09:37, 1 July 2014 (UTC)

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