[=X=]

Originally Posted by pdurrant

Clue:

Spoiler:

How about if one of them could see 12 towns? Would he have to guess about how many towns there were?

I kind of cheated and read omk3 first post. Once I read his logic, even though he didn't answer the problem I, knew I was wrong and also knew the answer, but at that point it was not a challenge since he gave me the direction I needed to solve the teaser.

Spoiler:

It looks like a dampened harmonic oscillator. Where the final answer is reached on day 5. If the day it is solved lands on an odd day the answer is 13, but if it lands on an even day the answer is 10.

It's been years since I've done this kind of math and though I do see the pattern I can't figure it out until I break open a math book.

So if the problem was solved on
Day 1=13 (11,12,13 are eliminated)
Day 2=10 (0,1,2 are eliminated)
Day 3=13 (8,9,10 are eliminated)
Day 4=10 (3,4,5 are eliminated)
Day 5=13 (only 6 and 7 are left)

By day 5 the only two numbers left is 6 and 7.