Thursday, September 20, 2012

Genius

Kadin was working on a math problem for his homework and asked for my help. He actually didn't bring the problem home but said he remembered it. He tried to explain it to me and it was something like this:
A jail has 100 cells. The guard comes in the first day and unlocks all the cells. On the second day he locks all the cells that are multiples of two. On the third day he unlocks all the cells that are multiples of 3 (or something like that, Kadin wasn't exactly sure) and so on. The question was, on the 100th day, which cells would be unlocked?

So we agreed there must be a pattern. Kadin had gone through and figured out
a few of the first cells and seemed to have a good grasp of how the problem worked. We decided that it had to do with how many factors a number had. It turned out that if a number had an even number of the factors, the cell would remain locked, but if it had an odd number of factors, it would be open. That was the pattern that emerged.

So then the question became which numbers have an odd number of factors? At first we thought it might have something to do with prime numbers or prime numbers multiplied by 2. Kadin kept testing out various ideas and theories. Until finally we got it: the only numbers that have an odd number of factors are squares. Squares seem so square that it is strange to think of them as uneven, but it turns out that the only way a number has an odd number of factors is if one pair of factors is the same number twice. Get it? Anyway, Kadin did.

I was so impressed how Kadin stuck with it and kept thinking and testing and following the logic. Rees is not like this at all and would never have the patience to mull over a math puzzle. All this time, Rees was off snacking and watching TV—he has a very easy load this year and not much homework.

Later that night, Greg and I were watching an episode of The Office when Rees came in to say goodnight. We pause the episode to chat. "What are you watching?" he asks. The Office. "Which episode?" He glances at the screen and says, "Oh, 'The Garage Sale.'" Then on his way out he adds, "the best pesto." The best pesto? Greg and I look at each other quizzically. Did he have pesto today? What is he talking about? We go back to the computer, press play, and the next line? "The best pesto."

Wow. My kids are so different from each other, but each one a genius.