at dinner, Monday...

My coworker's roommate was stumped by a problem on the MCAT that we'd discussed over lunch a few weeks ago. I had told them I was pretty sure my eleven-year-old could solve it.

So I decided to find out. At dinner on Monday I presented it to Robert.

"Let h(n) be the product of all even numbers less than or equal to n, so h(4) = 2*4, h(6) = 2*4*6, and so on. Is the smallest prime factor of (h(100)+1) ...
(a) less than 10
(b) between 10 and 20
(c) between 20 and 30
(d) between 30 and 40
(e) more than 40?"

Robert took about a minute, while chewing his sandwich.( Read more... )

Yellow and orange...

Sometimes I wish I were in the 21st century. Because then I'd have a digital camera and could post pictures to the internet and there'd be a base on Mars.

But anyway, on Monday Kate and Robert both passed their belt tests -- Kate is now a yellow belt and Robert is orange (second and third ranks, respectively -- they have purple, blue, green, brown, then black after this).

Kate had set herself the goal of getting a yellow belt before the summer was over, and now she has... and man is she a joy to watch. A nine-year-old with a cumulative ten years of experience in gymnastics, soccer, and ice skating, she's pretty coordinated and strong, and when you add brains and attention and enthusiasm... well, she's basically the whole package, as far as I can tell...