GeekDad Puzzle of the Week Solution: Easter Wars

Geek Culture

Not my dog. Notice the intelligence in her eyes. Image: Flickr/az1172

Despite the cerebrally-challenged wünderhund, we all survived Easter and even the week after. For those of you who missed it, last week’s puzzle was the following:

Not once, but twice during our Easter egg hunt, Shaggy Chewbacca, the lovely newest member of our family, destroyed Leif. Going about 25 mph, dog hits kid, kid flies, and silhouetted against the sun go eggs of every pastel hue.

What I wonder is if two hits was unlucky, lucky, or exactly as it should’ve been?

Imagine the egg hunting field as a 20×20 grid. Two kids roam randomly through the grid at a square per 10 seconds. And Shaggy Chewbacca, the indecisively named wünderhund, sprints through the grid once a minute during the 12-minute duration of the hunt — she effectively travels at light speed and so count her trips as taking zero time, like a laser. Here’s the tricky part: she always travels at 45-degree angles through the grid — as if drawing a straight line along the corner-to-corner diagonals through the “boxes” of the egg-hunt. But she has exactly equal chance of taking any diagonal.

If she crosses a box with a kid in it, eggs and tears fly.

How many times in twelve minutes should she hit a kid?

I have to admit that our winner this week out-solved me. I totally disregarded the chance of one dog trip hitting multiple kids. Mark, however, did not. Here’s what he wrote:

“There are 78 diagonals: 4 each of lengths 1 to 19 squares, and 2 of length 20 squares. With equal chance of taking any one diagonal, this gives the an average coverage of 10.256 squares per dash. There are 12 opportunities to hit 2 kids who could be in one of 400 squares. 10.256 * 12 * 2 / 400 = 0.61538
The pup will hit an average of 0.615 kids. There’s a fair chance at least one will be hit.”
And to the victor goes the $50 ThinkGeek gift certificate. For the rest of us, we can get $10 off a $50 order at ThinkGeek with code GEEKDAD44AF.
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