My chat riddle

[sanctus]

To those who were on the anniversary chat to solve and to al lthe others to solve as well:

Three people are caught by some native indians. The indians have five totem, three of which are blue and two of which are red. One person is attached to the first (sees no other totem), one to the second (sees the totem of the first person) and the third person is attached to the third totem (sees the totem of the first and second person). The inidans tell them that they are freed if they say to which totem they are attached to (ie. what color).they are not allowed to speak with each other.

After two hours nobody spoke, after other two hours still nobody and after other two hours someone speaks and they are freed. The question is who speaks and which color has the totem he is attached to?


Hint: two hour is equivalent to one reasoning.

[sanctus]

11 views! No solutions, nedd some more hints?

[Tormod]

Sorry...I am still stumped! A hint would help, yes.

[MortenS]

I have the solution I think...should I post the solution here, or send it as PM to sanctus?

[Tormod]

No, post it. I think the first one to solve any riddle should get the credit.

[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.

[sanctus]

As I read your PM first, before reading the post here I just confirm to the others, you are right.

I always thought it is funny that the one who doesn't see actually can say which color he is.

[MortenS]

quite fun, yes. I like puzzles like these.

[Gulielmus]

If you have any more i would love to take a shot at them. i came too late on this one.