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Guest Message by DevFuse
 

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Stamps and foreheads


Best Answer Prime, 07 February 2013 - 09:10 AM

I’ll try again.

Spoiler for not that long

 

Go to the full post


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16 replies to this topic

#1 bushindo

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Posted 31 January 2013 - 06:51 PM

This is based on bonanova's puzzle Colorful Foreheads

 

Here's a game that goes as in the following

* There is a host with 14 stamps, 7 red and 7 blue. There are five players- A, B, C, D, and E.
* In the beginning, the host affixes two stamps to each of the 5 players' head. The remaining 4 stamps go into the host's pocket. Each player can see the stamps on the remaining 4 players, but can not see his own stamps nor the four in the host's pocket.
* Starting from A to E (and then looping back to A and so on), the host asks if each player definitively knows his stamps distribution (RR, BB, or RB). If the player does not know, the host goes on to the next player. No guessing is allowed.
* The game goes as follows

1st turn- player A: I do not know
2nd turn- player B: I do not know
3rd turn- player C: I do not know
4th turn- player D: I do not know
5th turn- player E: I do not know
Host- Alright, to help you, I'll now reveal two stamps from my pocket. *At this point, the host pulls out two of the four stamps in his pocket and shows everyone. The game then continues as before*
6th turn- Player A: I do not know.


Question- what is the longest possible number of turns required before a player definitely knows his color?


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#2 CaptainEd

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Posted 31 January 2013 - 07:22 PM

Wow! This is a lot of cases, and I'll probably miss some in my exhaustive enumeration. Are you suggesting that we might be able to REASON this out, rather than list many dozens of cases? Thanks for the puzzle, by the way ^_^


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#3 bonanova

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Posted 31 January 2013 - 07:38 PM

Spoiler for For starters


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 CaptainEd

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Posted 31 January 2013 - 07:57 PM

Spoiler for but there's more knowledge earlier on, I think.


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#5 bonanova

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Posted 31 January 2013 - 08:38 PM

It may be fruitful to assume a distribution and then see how it can be determined.

 

Spoiler for first question


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#6 bushindo

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Posted 31 January 2013 - 08:38 PM

Wow! This is a lot of cases, and I'll probably miss some in my exhaustive enumeration. Are you suggesting that we might be able to REASON this out, rather than list many dozens of cases? Thanks for the puzzle, by the way ^_^

 

There are many cases on purpose. The reasoning should be straight forward with the proper tools and elimination procedure.


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#7 bushindo

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Posted 31 January 2013 - 09:27 PM

It may be fruitful to assume a distribution and then see how it can be determined.

 

Spoiler for first question

 

See the part in red. My calculations show that the players would definitely end the game during that phase for the starting case of all RB stamps.


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#8 CaptainEd

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Posted 31 January 2013 - 09:30 PM

I don't feel strong enough yet, but the Den is strong...

Spoiler for some useful observations about early learnings

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#9 bonanova

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Posted 31 January 2013 - 09:32 PM

A list of color combinations might be helpful.

They can be solved individually.

 

Spoiler for There are fourteen


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#10 CaptainEd

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Posted 31 January 2013 - 09:45 PM

It may be fruitful to assume a distribution and then see how it can be determined.

 

Spoiler for first question

 

See the part in red. My calculations show that the players would definitely end the game during that phase for the starting case of all RB stamps.

I'm confused, as often. I thought we were facing one particular run of this game, and we are seeking the one case and reveal for which A does NOT announce his stamps at step 6. The phrase "starting case of all RB stamps" makes me think we have to make a general solution for all runs of the game.


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