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[identity profile] writinghawk.livejournal.com Fri 2014-02-21 08:46
What a nice and curious problem. It's rather startling at first that the answers needn't be integers.

I don't even know that 5/3 is the best answer for the example above,

It seems most implausible that it isn't. Hmm, yes, let's see: in a better solution, each 5 stick must be cut into at most 2 pieces, obviously. The resulting (wlog) 14 pieces must be assembled into five 7-sticks so one 7-stick must get at most two pieces. One of these must be at least 3.5 long. Whichever 5-stick that came from, you had a length of 1.5 left over, which is too short.
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