At a competition, a group of 16 members is divided into 4 teams of 4 members each. The procedure of the competition is as follows:

Each team will be seated in a different room and after which every one will be given a cap either red or blue, i.e., total of 16 caps out of which 8 are red and 8 are blue and one from each room has to shout one of these words: Yes/No/OK and only once. They have to shout loud enough so that all other teams of their group can hear.

Then, one from each group(all 4 together) has to go to another room where they should tell the number of red and blue caps each of the other teams wore.

Before the competition started, all 16 of them are asked to devise a strategy together for every team to accomplish the task successfully. They are also told that they should not take the caps off their heads and should not talk to members of other teams until the competition is over.

Can you find out the strategy they used? It is known that all the 3 words have been shouted at least once and one of the guys said,"In this case, anyone one of four of us could have told you the distribution of hats even if we came here individually"?

Assume all their voices are indistinguishable.

(In reply to A question regarding the 'official solution' by Dej Mar)

1) OK is a unique case, so anyone can go to the final room

2) Its a particular case (Yes,No,No,OK) or (No,Yes,Yes,OK) 
where they can tell each others caps without attending
in the final room

3) Sorry, I forgot to mention this.
Strategy(1):
What they shouted, The colour of the cap who went to final room
Yes,Red -> 4 Reds
Yes,Blue -> 3 Reds, 1 Blue
OK -> 2 Reds, 2 Blues
No,Red -> 1 Red, 3 Blues
No, Blue -> 4 Blues

Strategy(2):
Yes,Red -> 4 Reds
Yes,Blue -> 4 Blues
OK -> 2 Reds, 2 Blues
No,Red -> 3 Reds, 1 Blue
No, Blue -> 1 Red, 3 Blues

Posted by Praneeth on 2008-08-26 02:27:31