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| This source might be added to the article if it adds anything. ] (]) 17:52, 30 June 2014 (UTC) | This source might be added to the article if it adds anything. ] (]) 17:52, 30 June 2014 (UTC) | ||
| :Thanks for the notice, but the article has better sources. Best wishes, --] (]) 18:07, 30 June 2014 (UTC) | :Thanks for the notice, but the article has better sources. Best wishes, --] (]) 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 | |||
| :{| class="wikitable" style="text-align:center" | |||
| |- | |||
| | style="background:#FFEBAD;" align="left" | '''number of drawer''' || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 | |||
| |- | |||
| | style="background:#FFEBAD;" align="left" | '''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. ] (]) 08:05, 1 July 2014 (UTC) | |||
Revision as of 08:05, 1 July 2014
 | This article contains a translation of Problem der 100 Gefangenen from de.wikipedia. |
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)
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