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Smart prisoners always get a break (Posted on 2002-08-27) Difficulty: 4 of 5
100 prisoners are put into solitary cells. There's a central living room with one light bulb; the bulb is initially off. No prisoner can see the light bulb from his or her own cell. Every day, the warden picks a prisoner at random, and that prisoner goes to the central living room. While there, the prisoner can toggle the bulb if he or she wishes. Also, the prisoner has the option of asserting the claim that all 100 prisoners have been to the living room. If this assertion is false (that is, some prisoners still haven't been to the living room), all 100 prisoners will be shot for their stupidity. However, if it is indeed true, all prisoners are set free and inducted into MENSA, since the world can always use more smart people. Thus, the assertion should only be made if the prisoner is 100% certain of its validity.

The prisoners are allowed to get together one night, to discuss a plan. What plan should they agree on, so that eventually, someone will make a correct assertion?


  Submitted by levik    
Rating: 4.3636 (11 votes)
Solution: (Hide)
The prisoners need to designate a "counter" from among themselves.

Everyone who is not the counter, upon coming to the living room will turn the light on if

  • The light is currently off, and
  • This is their first time turning on the light

    The counter, starting with a count of zero, upon coming to the living room, will do the following:

  • If the light is on, he will turn it off, and add one to his count.
  • If the light is off, he will not simply leave without touching the light or changing the count.

    When the counter's count reaches 99, he knows that 99 other people have been to the living room. Since he has also been there, he can safely announce that all the prisoners have visited the living room.

  • Comments: ( You must be logged in to post comments.)
      Subject Author Date
    Solutionmy solution, hope everyone likes it ;-)vivek2008-06-10 19:36:08
    Smart prisoners always get a break 2axf2007-02-12 09:47:00
    re(3): This seems really easy...Gamer2007-01-15 14:06:53
    re(2): This seems stupidly easy...thegnome542006-06-04 16:50:28
    re: This seems stupidly easy...Vernon Lewis2006-02-09 18:03:20
    This seems stupidly easy...thegnome542006-02-09 16:00:40
    SolutionNo SubjectBryson2005-12-16 11:02:39
    Another solutionRajal2004-08-04 14:47:56
    Possibly ...Lawrence2003-09-01 10:10:51
    SolutionPossible solutionDacre2003-08-29 12:25:18
    re: My solutionGamer2003-06-25 03:14:52
    SolutionMy solutionragnar2003-01-22 10:41:04
    Somthing about dividing the prisoners in half...Matt2002-08-28 05:35:39
    re(4): An impractical solution...TomM2002-08-28 00:40:38
    re(4): An impractical solution...levik2002-08-27 17:39:41
    i know this is wrongKristina2002-08-27 15:18:11
    re(3): An impractical solution...Jim Lyon2002-08-27 10:54:44
    re(2): An impractical solution...levik2002-08-27 09:26:28
    re(3): An impractical solution...levik2002-08-27 09:24:57
    re: An impractical solution...Jim Lyon2002-08-27 09:03:29
    re(2): An impractical solution...friedlinguini2002-08-27 08:37:38
    Questionre: An impractical solution...levik2002-08-27 08:27:46
    SolutionAn impractical solution...friedlinguini2002-08-27 06:15:44
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