simont: A picture of me in 2016 (Default)
simont ([personal profile] simont) wrote2014-04-23 10:49 am

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/.

[identity profile] angoel.livejournal.com 2014-04-26 07:03 am (UTC)(link)
I'm not sure you need to go all the way up to 120 - when putting together this dissection, I worked to maximise all stick lengths, but if you accept that the lower bound is 41/10, you can shorten some stick lengths to give a denominator of 10 throughout (which, as a bonus, gives a simpler dissection).

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)
Edited 2014-04-26 10:28 (UTC)