Unsolved problem writeup
Thanks to everyone who commented on my previous entry with proofs, software and other useful comments. I think I've now taken the investigation of this problem as far as I have the energy to, at least for the moment. A collection of all the useful things I know about it, including a big pile of data, is now up on a web page: http://www.chiark.greenend.org.uk/~sgtatham/matchsticks/.
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That is, it violates the stronger form of it on which my search program depends: although the denominator of the minimum fragment size is less than n, the lowest common denominator for the whole solution is not, since in this case it's 120. My program searches whole-solution denominators up to n, and the best it found for this instance was a min fragment of 4.
That suggests that other yellow cells may not have the values they should have either...
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Of course, this does mean that your program should probably be looking for larger denominators...
Best known dissection should be equal to 41/10:
Divide 9 sticks size 29:
4 x (41/10 + 41/10 + 41/10 + 41/10 + 42/10 + 42/10 + 42/10)
3 x (48/10 + 48/10 + 48/10 + 48/10 + 49/10 + 49/10)
2 x (49/10 + 49/10 + 49/10 + 49/10 + 49/10 + 45/10)
Reassemble as 29 sticks size 9:
16 x (41/10 + 49/10)
12 x (42/10 + 48/10)
1 x (45/10 + 45/10)
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