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This week's Challenge Question:
A customer goes into a jewelers shop and lays 8 chain segments on the counter. The segments are 30, 20, 17, 13, 9, 6, 3, 2 links long long, and each link is 1cm. The customer asks that they be assembled into a continuous chain 100 links long, by cutting and re-joining links as necessary. If it takes 1 minute to cut and open a link, and 2 minutes to weld it closed (ignore the time taken to pick-up, thread or set down the link), what is the least time in which the jeweler can complete the task?
Thanks to SlideRuler for providing us with this Challenge.
And the Answer is...
There are 8 sections. If he simply opened the end link of a section and attaches it to another section, he would have to do this 7 times to make a continuous length taking 21 minutes. If he cuts the 6 link section into separate links, he will have enough cut links to join the 7 remaining sections, taking 18 min. He can do even better, by cutting the 3 and 2 link sections into separate links, and use the 5 cut links to join the 6 remaining sections. Time taken in this case is 15 min.
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