Puzzles

The order in which A and B spoke is important.

Each of the logicians can see two numbers and knows that her number is either the sum of or the difference between these numbers.

The only way in which A could've known her number was if B and C had the same number (as the difference would be 0, not positive). So after A speaks, B knows that B\(\not=\)C.

There are two ways in which B could know her number: (1) if A=C, or (2) if the information revealed by A removed one of the options.

(1) is not possible, as this would mean that B is the sum of A and C and therefore even (but 15 is odd.

Therefore (2) must have happened. Learning B\(\not=\)C removed one of B's options, so B=C must have been one of B's options. This is only possible if A=2C, giving B's options as being equal to C or 3C.

As B cannot be C, B must therefore be 3C, so the numbers are: A=10, B=15, C=5.