Two players, A and B, both have the number 12 written on their foreheads.

Each one sees the number on the forehead of the other one, but does not know his own number.

A third person, C, tells them that the sum of their two numbers is either 24 or 27 and that it concerns only two positive integer numbers greater than zero.

Then C asks again and again alternating A and B whether they can determine the number on their foreheads.

A: No.
B: No.
A: No.
B: No.
A: No.

After how many “no"s, can one figure out his own number? Or there is no way, after all?

This is a specific case of Hugo's problem from several years ago,
<a href="show.php?pid=4051">The Undiscovered Numbers</a>

It looks a little different, because you know the other person's number and not yours, but it is really the same problem.

Posted by Steve Herman on 2008-12-17 12:44:05