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#1 Kornrade

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Posted 07 December 2010 - 01:09 PM

This is my favourite brain teaser, and one of the most difficult that I know. I apologize if it has been posted before and I missed it.

A team of 15 takes part in a contest. They know each other and all the rules of the contest, and they have time to make their strategy before the actual contest starts.

The rules of the contest are:

1. The players sit in a circle, so that everybody sees everybody. Then the players are blindfolded.

2. On each player's head, either a red or a blue cap is placed. The colour of the cap is determined completely arbitrarily, e.g. by coin toss.

3. The blindfold is removed, and everybody has to write on a piece of paper the answer to the question "What is the colour of your cap?". The answer must be "RED", "BLUE" or "---". Everybody has to write down their answer at the same time.

4. Everybody shows the paper at the same time.

5. The players do not cheat. (They do not exchange information through words, utterances, signs, facial expressions, delays in writing their answer, etc.)

The procedure of the contest is done only once. The team wins the contest if at least one answer is correct and no answer is incorrect. "---" is considered a neutral answer, neither right nor wrong.

Examples:

if team member #12 correctly answers RED, and everybody else answers "---", they win.

if all members answer correctly (RED/BLUE), except for member #12 (who said RED and had blue), they lose.



Which is the strategy with the biggest chance to win, and how high is that chance?
Have fun!


[P.S.] For those who know Romanian, this and many other brainteasers are to be found at www.chichitza.com and www.chichitza.com/forum

As for chess, a section in English is www.chichitza.com/chess.html . It contains puzzles and studies. Some studies may be more difficult for computers than for humans :D
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#2 KlueMaster

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Posted 07 December 2010 - 02:17 PM

This is my favourite brain teaser, and one of the most difficult that I know. I apologize if it has been posted before and I missed it.

A team of 15 takes part in a contest. They know each other and all the rules of the contest, and they have time to make their strategy before the actual contest starts.

The rules of the contest are:

1. The players sit in a circle, so that everybody sees everybody. Then the players are blindfolded.

2. On each player's head, either a red or a blue cap is placed. The colour of the cap is determined completely arbitrarily, e.g. by coin toss.

3. The blindfold is removed, and everybody has to write on a piece of paper the answer to the question "What is the colour of your cap?". The answer must be "RED", "BLUE" or "---". Everybody has to write down their answer at the same time.

4. Everybody shows the paper at the same time.

5. The players do not cheat. (They do not exchange information through words, utterances, signs, facial expressions, delays in writing their answer, etc.)

The procedure of the contest is done only once. The team wins the contest if at least one answer is correct and no answer is incorrect. "---" is considered a neutral answer, neither right nor wrong.

Examples:

if team member #12 correctly answers RED, and everybody else answers "---", they win.

if all members answer correctly (RED/BLUE), except for member #12 (who said RED and had blue), they lose.



Which is the strategy with the biggest chance to win, and how high is that chance?
Have fun!


[P.S.] For those who know Romanian, this and many other brainteasers are to be found at www.chichitza.com and www.chichitza.com/forum

As for chess, a section in English is www.chichitza.com/chess.html . It contains puzzles and studies. Some studies may be more difficult for computers than for humans :D


Assuming that there is no limitations on number of caps of either color (i.e., they might be wearing all red or all blue), it would be wise to
Spoiler for follow this strategy

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#3 chilepepper

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Posted 07 December 2010 - 03:25 PM

Assuming that there is no limitations on number of caps of either color (i.e., they might be wearing all red or all blue), it would be wise to

Spoiler for follow this strategy


I came up with a similar solution except
Spoiler for

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#4 methinks

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Posted 07 December 2010 - 04:06 PM

Assuming that there is no limitations on number of caps of either color (i.e., they might be wearing all red or all blue), it would be wise to

Spoiler for follow this strategy

That strategy is not really required:
Spoiler for because

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#5 Egghead

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Posted 07 December 2010 - 06:17 PM

Spoiler for off the wall

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#6 wolfgang

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Posted 07 December 2010 - 07:17 PM

Is it allowed to only one person to change his place?
If yes,,It will be very easy.
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#7 SteveK

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Posted 07 December 2010 - 07:50 PM

Seems that Fast Reply is not working for me. Sorry if this appears multiple times.


Spoiler for I don't think this answer would be considered cheating under the specified rules

Edited by SteveK, 07 December 2010 - 07:51 PM.

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#8 Kornrade

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Posted 07 December 2010 - 07:52 PM

Spoiler for off the wall

Seems that Fast Reply is not working for me. Sorry if this appears multiple times.


Spoiler for I don't think this answer would be considered cheating under the specified rules


Remember:
5. The players do not cheat.

To put the problem another way, all players of the team are housed in separate rooms. Everyone is informed about the colour of all others' caps by an arbiter. There is absolutely no possibility of learning more information than those colours.

Edited by Kornrade, 07 December 2010 - 07:56 PM.

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#9 bushindo

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Posted 07 December 2010 - 09:02 PM

Remember:
5. The players do not cheat.

To put the problem another way, all players of the team are housed in separate rooms. Everyone is informed about the colour of all others' caps by an arbiter. There is absolutely no possibility of learning more information than those colours.


How about this strategy
Spoiler for

Edited by bushindo, 07 December 2010 - 09:08 PM.

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#10 amateur

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Posted 07 December 2010 - 09:12 PM

That strategy is not really required:

Spoiler for because


Spoiler for Is it really a random guess?

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