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[personal profile] simont Sat 2014-03-08 00:32
Ian has written a fairly shiny search program which confirms your guess that the best dissection is not always equal-sized. 7 into 4 has minimum fragment 5/3, which is not an integer fraction of either stick length. So much for my conjecture.

(I leave the exact dissection of 7 into 4 as an exercise, but it shouldn't be hard given the minimum length :-)
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