GeekDad Puzzle of the Week — Sleeping Bag Conundrum

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After returning this morning from a sleep-over/locking event with Max and his scouting troop at a local museum, I am rather tired. Not because it was loud, late, and full of energy — that is to be expected. I am tired this morning because I was up all night thinking about, of all things… sleeping arrangements.

SleepingBag_StoryYou see, the 32 scouts in attendance slept on a standard 8×8 chessboard. Each scout could take up 2 horizontally or vertically adjacent spots, and all of the spots were taken. To make sure that the chaperoning parents could quickly get to any child if needed, at least every other row’s horizontal edge must be unobstructed. Finally, the row closest to the dinosaur skeleton exhibit had to be made up out of the four oldest scouts, all laying horizontally. (I guess that there was a movie where people spent the night at a museum that involved a T-Rex skeleton?)

It doesn’t matter who sleeps where necessarily, just the pattern of horizontal and vertical scouts. Each solution can have at most two contiguous rows, so that any scout can be accessed. Here is an example where that is observed, and where it isn’t observed:

Observed
No more than two rows are blocked with scouts

NotObserved
More than two rows are blocked with scouts

This week’s puzzle, and the conundrum that kept me up most of last night: how many unique patterns of horizontal and vertical scouts could be laid out respecting the “access” rule, and having the “border row” of horizontal scouts at one end?

As always, please send your responses in to GeekDad Central. All correct (or at least reasonably well-reasoned) responses will be entered into a drawing for this week’s fabulous prize: a $50 Gift Certificate from our friends at ThinkGeek!

Good luck, and happy puzzling!

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