I think this belongs in set theory? I may be wrong though. I always enjoy a good math problem, and my niece made me think of something that I couldn't figure out an easy way to get an answer.(adsbygoogle = window.adsbygoogle || []).push({});

She likes making those plastic bracelets with that plastic chord with the different colors and weaving them into keychains and such (like the girl was selling on napoleon dynamite). she has a bunch of different spools with different colors she uses and makes a ton of them for her friends/family etc.

so as she was sitting there working on some i saw her measure out really long strands. one of the colors she wanted to use on the spool was too short so she tied two shorter pieces together. i was confused but i watched her work and she weaved it and when she got to the part with the knot, she just skipped over it and left a section of straight pieces and continued the weave below it so she had a long bracelet with a straight limp part in the middle where the knot was. so i was like...what are you going to do here. and then she cut out the knot and tied the ends off of the two resulting pieces and had 2 thingamabobs...I asked her why she did this, and she said when she's weaving, she doesn't like to stop and just gets in the groove and as long as it's about 4 inches thats good for a keychain.

so i was thinking about this over the weekend and it started bugging me and i was thinking how would she do it if she had multiple short pieces so different colors would have multiple knots, she'd have to try to line up where the knots landed if she could to get the most efficient use of her chord. and i was thinking there has to be some mathematical way to figure out the best way to use her remaining chord so she could tie it all and weave away, and then just cut out the knots, by having the knots line up as much as possible.

so i wrote it all out on a piece of paper thinking I'd figure out some efficient way to do this and quickly realized i stumped the crap out of myself...so it's been bugging me to the point where i want to take to the internets and see if it's even possible or did i just dream up some impossible scenario...

here's what i was trying to figure out.

spools (color, and amount of inches on each spool left)

yellow:15,25,8,6

red:19,15

blue: 12,25,11

green: 15, 16, 9

how can she figure out the best way to make like 30 inches of total gifts, but none being less than 4 inches?

and if she wanted to use 3 colors, or all 4...or if she had more colors...etc

so like she would have a 2 color weave and wants 34ish inches of weave, number of pieces doesn't matter, just must be longer than 4, and you can have leftover, but pieces less than 4 will be tossed...

r----19-----------x----15-----x

y--25(cut to 19)--x-8---x--6--x

------------------c-----c-----c

and her end result would be 3 jewelry pieces of 19, 8 and 6 with some loss around the cuts obviously but i think that can be ignored mainly would there be a way to figure out what the best layout is for a color combination to get the best lineup of cuts to make as much weave length as she can, not caring how many pieces as long as they're greater than 4 inches, just the length she's weaved?

is this even possible, i've stumped myself something serious thinking about it...like it seems like maybe you'd have to brute force it or something writing up something to try everything... but it seems like there may be multiple sets that can be acceptable answers and i wrote all this down like i was going to come up with some clever solution and put my niece to work in a bracelet factory, but i furrowed my brow and it hasn't unfurrowed since...

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# Plastic bracelet making problem i dreamed up talking with my niece

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