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Lenny Conundrum - Round #421

I found this on and was interested:

Samrin has been having trouble with a very hungry Babaa eating all the grass and leaving none for the other Petpets. He decided to separate the Babaa from the others, but the only area Samrin had left in his field was a hexagonal patch, each side measuring 40 yards.

Samrin tied the Babaa to a post in one corner of the field using a 50 yard rope, and he knows it takes the Babaa 13 minutes to eat 1 square yard of grass.

The first question is how to find the area defined by a 50 unit arc within the hexagon. You can do the fancy math if you want but I prefered to model this in SketchUp as it's way faster this way.

(click to expand)

So if we know the area is 2447.43 square units then the rest is just details.

The goat consumes 1 square yard in 13 minutes which means that in a day, which is 1440 minutes for reference (60 minutes * 24 hours = 1440) then he'll eat 111 square units (as 1440 / 13 = 111).

So he'll finish the lawn in 22 days (2447 square units / 111 square units per day).