Science Forums 2

[MortenS]

Ok, I did post a copy to Sanctus as well...pick my solution apart!

The short version: The first person speaks up at the third contemplation, and says his totem is colored blue.

Here is how I arrived at the answer (eliminated combinations in red)

There are 10 possible combinations of 3 blue totems and 2 red totems.
(RRBBB, BRRBB, BBRRB, BBBRR, RBRBB, BRBRB, BBRBR, RBBRB, BRBBR, RBBBR)

Of these 10, one of them, the one with the first two totems being red, the third person would have figured out that his totem was blue. Since the third person did not speak up, this solution can therefore be eliminated.

At 2nd reasoning, there are 9 possible combinations, with 6 different combinations for the first 3 totems.

( BRRBB, BBRRB, BBBRR, RBRBB, BRBRB, BBRBR, RBBRB, BRBBR, RBBBR)

If the second person sees a red totem, the probablity that his totem is red is 0, and the probability that his totem is blue is 1. Since nobody said anything, we can eliminate the solutions where RBB and RBR are the combinations of the first 3 totems.

For the third reasoning we are left with the following possible solutions:

(BRRBB, BBRRB, BBBRR, BRBRB, BBRBR, BRBBR)

The second person sees only a blue, and can not be sure whether his totem is red or blue.
The third person see either two blue, or a blue or red, and can not be sure whether his totem is blue or red.
Only the first person can be sure that his totem is blue, so my proposal is that it is the first person that speaks up, and say that the color of his totem is blue.