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A Show Of Hands


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17 replies to this topic

#1 plainglazed

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Posted 14 May 2012 - 01:16 PM

Each of eight logicians has a unique positive integer less than 100 stapled to their foreheads. They stand in a circle facing one another so every logician can see everyone's number, save for their own. Each logician must discern their number and raise their hand. After all logicians have raised a hand, they must then all declare their number in unison. What strategy (within the assumed spirit of these types of puzzles) might they employ such that all are correct?

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#2 Time Out

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Posted 14 May 2012 - 03:10 PM

Am guessing that they can agree on a system of communication beforehand


Spoiler for ?Show of Hands


I like the image of the "stapled to head"
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#3 plainglazed

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Posted 14 May 2012 - 03:33 PM

I thought for sure I mentioned in the OP that they were attending the Arctic Circle of Logicians annual Fresh Air/Fresh Ideas Seminar and were all wearing mittens. Apparantly not, so your answer does indeed fit within the constraints of the OP, Time Out. But for grins, let's do assume the logicians are all wearing plain white mittens.
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#4 bushindo

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Posted 14 May 2012 - 03:49 PM

I thought for sure I mentioned in the OP that they were attending the Arctic Circle of Logicians annual Fresh Air/Fresh Ideas Seminar and were all wearing mittens. Apparantly not, so your answer does indeed fit within the constraints of the OP, Time Out. But for grins, let's do assume the logicians are all wearing plain white mittens.


When you say 'numbers less than 100', do you mean 'integers less than 100 but larger than 0'? Also, can a number be repeated?

Edited by bushindo, 14 May 2012 - 03:54 PM.

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#5 mewminator

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Posted 14 May 2012 - 04:43 PM

Spoiler for A possible way of doing it

or I could go for the simpler way
Spoiler for simply

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#6 plainglazed

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Posted 14 May 2012 - 05:01 PM

hey bushindo - right you are, rewrote this this a.m. and forgot that bit. hadn't saved my .txt draft and Microsoft was kind enough to update and reboot my machine last night. thanks and sorry

and sorry, too - no blinking in morse code, looking in the reflection of the irises to your right, hoof stomping, shouting the number across from you in pig latin, etc., etc...
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#7 Molly Mae

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Posted 14 May 2012 - 05:12 PM

Once a hand is raised, can it be put down? Or would that qualify as illegal communication?
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A recipe for honey-pickled apples


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Spoiler for Molly's Rules to Live By

#8 plainglazed

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Posted 14 May 2012 - 05:15 PM

hey Mo Ma - no, once a hand is raised that is the only bit of info the rest of the group can directly discern from that logician.
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#9 bushindo

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Posted 14 May 2012 - 05:33 PM

Each of eight logicians has a unique positive integer less than 100 stapled to their foreheads. They stand in a circle facing one another so every logician can see everyone's number, save for their own. Each logician must discern their number and raise their hand. After all logicians have raised a hand, they must then all declare their number in unison. What strategy (within the assumed spirit of these types of puzzles) might they employ such that all are correct?

EDIT


Here's an attempt.
Spoiler for Solution

Edited by bushindo, 14 May 2012 - 05:35 PM.

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#10 bushindo

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Posted 14 May 2012 - 06:17 PM

I just want to come back and say that this is a really well designed puzzle. I didn't explain the rationale behind the solution before, and so here it is

Spoiler for rationale

Edited by bushindo, 06 July 2012 - 07:35 PM.

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