GeekDad Puzzle of the Week: Potato Hamster at Large

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"My enemy, my foe, is an animal. In order to conquer the animal, I have to learn to think like an animal. And, whenever possible, to look like one." — Carl Spackler, Caddyshack. Image: Flickr/cdrussorusso cc license

Potato Hamster is at large. On Sunday morning, GeekDad Day, we found the top exercise wheel portion of her cage on the floor, leaving a hole, and the hamster was nowhere to be found. The folks at the pet store recommend placing cookie sheets with a light coating of flour and a peanut-buttered apple in each room to discover her general whereabouts and then a small trashcan with another peanut-buttered apple in the bottom, stairs of books leading to its lip to catch Potato. My Facebook friends recommend getting a cat.

What I wonder is how long we should keep hope alive. What are the day-by-day chances we’ll catch Potato Hamster?

There are four rooms where she might be, plus the heating system, plus outside, all with equal probability. If she’s outside or in the heating system, she’s toast. (We refer to this as “having an adventure.”) Every night, we put flour-coated cookie sheets in three rooms and a garbage can trap in the fourth; if she’s in a room, there’s an 80 percent chance her tracks will show up on a sheet or she’ll end up in the can. If her tracks show up on a sheet, add 20 percent to our overall chance of capturing Potato. If she’s in the can, game over. Of course, every night she’s on the move and re-randomizes her probability of being in the heating system or outside, which is also game over.

What are our daily chances of recapturing Potato?

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