Posted 31 March 2008 - 05:03 AM

Here is what I think you are going for:

a is me, b is 5 and c is 13.

I could have 8 or 18, so I don't know.

b sees 8/13 or 18/13 and knows he can have 5/21 for my 8, or 5/31 for my 18. Giving him 5, 21 and 31 to pick from, so he doesn't know.

c sees 8/5 or 18/5 and knows he can have 3/13 for my 8, or 13/23 for my 18. He also takes into account what b is thinking, and adds into the mix 13/29, 3/39, 23/39, and 13/49. Giving him 3, 13, 23, 29, 39, and 49 to pick from, so he doesn't know.

Since I realize that the number of possibilities will continue to increase indefinitely, I concentrate on the lowest possible number and work from there. If c thinks he can possibly have a 3, and b has a 5 (also being the smallest he believes possible for himself) then my number could be a 2 or an 8, so I don't know.

b starts to think the same way, and realizes that I think I could have a 2, and c thinks he could have a 3, making his number a 1 or a 5. He doesn't know.

c, also realizing it, gets a 2 from me and a 1 from b, giving him a 1 or a 3. He doesn't know.

Me, now, I get left with a 1 and a 1, making mine a 2 if everyone really had those low number, but alas, they do not, so I don't really know.

b, hearing that I don't know, knows that the whole "lowest number" thing didn't pan out.

I guess this could continue until you exhausted the possibilities up the ladder of numbers, but I'm not really seeing how...

Could you give a bigger hint?