GeekDad Puzzle of the Week Solution: Maximize Bedtime Utility

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Flickr user JD Hancock, CC license

Howdy ho, sleepy puzzlers. Let me admit this up front: this past week’s puzzle was fairly abstract (some would say abstruse). Here’s the recap: You’re putting the kids to bed and the optimal bedtime ebbs or flows according to the following rules:

• It’s a complete nonstarter to suggest bedtime before Sprout’s Good Night Show host Nina (who, coincidentally, is a zombie) does Lucy Light My Way at 7:30pm. And my wife and I become werewolves at 9:30pm sharp.

• Every book read is worth 10 minutes in utility to my kids. However, while the first book costs my wife and I only 2 minutes of utility, every subsequent book costs another additional minute.

• Parents burn 15 minutes of utility to ensure proper teeth brushing, face washing, and loo using.

• Asking to play chess gains my 5yo 30 initial minutes of utility, which, unfortunately, decays at a rate of 1minute-per-1minute, as while we play chess, my 3yo bugs my wife who would otherwise be hiding in the back room re-watching West Wing DVDs on her laptop.

• The kids have learned that we feel guilty about neglecting our yellow lab, Gus, whom we had before we had kids. Kids earn 16 minutes of utility by offering to pet Gus and tell him he’s a good dog. Every subsequent offer earns them the square root of the previous utility.

What I meant to have happen is to split the possible parental/child bedtime window of 7:30pm-9:30pm in half and then adjust the 8:30pm starting point based on the remaining rules. For example, we would read books until the gain in utility became negative, i.e. until parental displeasure magnified past the 10 minutes of utility the kids gain per book.

With this in mind, the rules unfortunately bring us to the max bedtime of 9:30pm, which has proved fairly verifiable by observation lately. (However, I posit that the bedtime landscape will undergo paradigm shift with the fast upcoming start of school.) A couple of you intuited the rules as I intended them. Many of you didn’t but provided solutions that were correct according to your own assumptions, and I counted these as correct too.

The most entertaining answer was from John who pointed out that I missed “60 time units for parental units to narfle the garthock, and 15 time units for post narfle consuming of mass quantities.” I guess we all have different words for this in our different households.

But the winner of this week’s $50.00 ThinkGeek Gift Certificate is Sean, who found two nodes of maximal utility, one driven mostly by parents at 7:45 and one driven mostly by kids at 8:17 (again, using some assumptions that were different than mine, but doing the math very well.) For everyone else, use the code GEEKDAD81AD starting August 1 for $10.00 off your next order of $50.00 or more at ThinkGeek.

Check back Monday for what will hopefully be a less abstract/abstruse puzzle from the omnipotent Dave.

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