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PUZZLET 118

Twenty Bricks

A brick's dimensions are 3 x 4.5 x 9. You have twenty of them. Using all twenty, lay them end to end. Each brick can present its 3, 4.5, or 9 length sides at random. Many lengths can be made in this way.
Bricks
Are there any of the lengths between 60 and 180 divisible by 1.5 which cannot be made from twenty bricks? Which particular length can be made in the greatest number of different ways? Enumerate each way for this special case.


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Last Updated: January 14th, 2010.