4 ms·

Hardly the hardest. Here's a harder: http://justinpombrio.net/tell/prisoner-lightbulb.html http://justinpombrio.net/tell/prisoner-lightbulb.html EDIT: Also, f

Hardly the hardest. Here's a harder: http://justinpombrio.net/tell/prisoner-lightbulb.html http://justinpombrio.net/tell/prisoner-lightbulb.html EDIT: Also, for anyone stuck on the three gods puzzle, the three sisters puzzle is a good stepping stone: http://mathpuzzlewiki.com/index.php?title=Three_princesses http://mathpuzzlewiki.com/index.php?title=Three_princesses

hurin 12y ago
Is there a link for a solution to your variant (of the prisoners and lightbulb problem)?
- zatkin 12y ago
  The original problem is on a website that also contains the answer (in a red, dash bordered box) [1]. [1] - http://www.cut-the-knot.org/Probability/LightBulbs.shtml http://www.cut-the-knot.org/Probability/LightBulbs.shtml
  - hurin 12y ago
    I know the original problem. I'm curious how he obtains a deterministic solution for the version where the warden can switch the light-bulb state at random (excerpt below). “I reserve the right to flip the light on or off between interrogations up to 12 times in total.” Maybe it's poorly worded?
    - justinpombrio 12y ago
      You mean the Easy++ problem? The solution isn't very different from the solution to Easy (i.e. the original problem); it just takes longer to run. For the Hard problem, you're on your own. The wording is very careful :-)
      - hurin 12y ago
        >> “I reserve the right to flip the light on or off between interrogations up to 12 times in total.” > The wording is very careful :-) Do you mean he can flip the switch 12 times in total between all interrogations? Or that between every interrogation he can flip the switch up to 12 times. That's what I mean by poorly worded.
        justinpombrio 12y ago
        The former, hence the phrase "in total", and the number 12 instead of 1.
        hurin 12y ago
        > The former, hence the phrase "in total", and the number 12 instead of 1. It wasn't very clear. >> You mean the Easy++ problem? The solution isn't very different from the solution to Easy (i.e. the original problem); it just takes longer to run. Btw what's the run-time on your easy++ solution? - I think the run-time on the solution to the regular problem with a single counter is around ~26 years, so all your prisoners will die before they can get released unless you're doing something more clever than the basic solution. Also I'm not sure I understand the difference between your Easy and Hard problems? I assume the prisoner who is not interrogated with the other inmates just estimates the run-time for their solution and waits (which I think is part of the original problem anyway ? )

hurin 12y ago

Is there a link for a solution to your variant (of the prisoners and lightbulb problem)?

zatkin 12y ago
The original problem is on a website that also contains the answer (in a red, dash bordered box) [1]. [1] - http://www.cut-the-knot.org/Probability/LightBulbs.shtml http://www.cut-the-knot.org/Probability/LightBulbs.shtml
- hurin 12y ago
  I know the original problem. I'm curious how he obtains a deterministic solution for the version where the warden can switch the light-bulb state at random (excerpt below). “I reserve the right to flip the light on or off between interrogations up to 12 times in total.” Maybe it's poorly worded?
  - justinpombrio 12y ago
    You mean the Easy++ problem? The solution isn't very different from the solution to Easy (i.e. the original problem); it just takes longer to run. For the Hard problem, you're on your own. The wording is very careful :-)
    - hurin 12y ago
      >> “I reserve the right to flip the light on or off between interrogations up to 12 times in total.” > The wording is very careful :-) Do you mean he can flip the switch 12 times in total between all interrogations? Or that between every interrogation he can flip the switch up to 12 times. That's what I mean by poorly worded.
      - justinpombrio 12y ago
        The former, hence the phrase "in total", and the number 12 instead of 1.
        hurin 12y ago
        > The former, hence the phrase "in total", and the number 12 instead of 1. It wasn't very clear. >> You mean the Easy++ problem? The solution isn't very different from the solution to Easy (i.e. the original problem); it just takes longer to run. Btw what's the run-time on your easy++ solution? - I think the run-time on the solution to the regular problem with a single counter is around ~26 years, so all your prisoners will die before they can get released unless you're doing something more clever than the basic solution. Also I'm not sure I understand the difference between your Easy and Hard problems? I assume the prisoner who is not interrogated with the other inmates just estimates the run-time for their solution and waits (which I think is part of the original problem anyway ? )