Contestants and stamps

salem_ohio · 2017-01-16 21:52:44

During a game show, the host has placed three contestants (A, B, C) in a closed room. The host places one stamp on each of the contestant’s forehead in such a way that each contestant can only see the other stamps, but not his own. He places a white or black stamp to the forehead of A, a red or green stamp to B and a yellow or blue stamp to C. He then asks each of them to simultaneously write on a piece of paper the color of the stamp they think that they have on their own forehead. The only choices that are permitted are, either a color, or "I don't know". The contestants will win if at least one of them correctly guesses his own color, but with the restriction that no one must not give a wrong answer (for example, if 2 of the 3 contestants reply "I don't know" and the 3rd one guesses correctly, they win the contest).
The host allows the contestants to discuss and coordinate for a few minutes, before the placement of the stamps, in order to decide on a strategy. What is the optimum strategy that will give them the biggest chance to win?

anna_gg · 2017-01-21 02:41:52

...must be something with mod(3).

I also read that these types of problems are solved by using Hamming codes
No idea how!!

Last edited by anna_gg (2017-01-21 06:35:08)

iamaditya · 2017-01-26 05:18:09

salem_ohio wrote:

The host places one stamp on each of the contestant’s forehead in such a way that each contestant can only see the other stamps, but not his own.

What do you mean by the other stamps? Are they the stamps on the other 2 person's forehead. If that is to be then they will discuss what they could see on the other two person's forehead and then everyone can tell the correct answer.

Math Is Fun Forum

#1 2017-01-16 21:52:44

Contestants and stamps

#2 2017-01-21 02:41:52

Re: Contestants and stamps

#3 2017-01-26 05:18:09

Re: Contestants and stamps

Board footer