My puzzle-a-day calendar had a magic square today – a three by three grid in which every row, every column, and both main diagonals add up to the same value, which is to determined. They give you three numbers to start:

12 __ __

__ 10 __

7 __ __

I gave up quickly and peeked at the answer, which reads: “To start, since the left-to-right diagonal and the bottom row add up to the same amount” [okay, with ya so far] “we can work out the value of the bottom middle cell. It must be 12 + 10 - 7 = 15.” Uh … why? I mean, I see where the three numbers on the left side of the equation come from, but why is that what you do with those three numbers?

TIA.

(and please stop laughing.)