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## Question

A man bought 12 lengths of chain, as shown, and asked the local blacksmith to forge them into an endless chain of 100 links.

The blacksmith said the cost for splitting and joining small links would be \$3 each; for large links it would be \$4 each.

How much should the man have to pay to have the endless chain made?

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A man bought 12 lengths of chain, as shown, and asked the local blacksmith to forge them into an endless chain of 100 links.

The blacksmith said the cost for splitting and joining small links would be \$3 each; for large links it would be \$4 each.

How much should the man have to pay to have the endless chain made?

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A man bought 12 lengths of chain, as shown, and asked the local blacksmith to forge them into an endless chain of 100 links.

The blacksmith said the cost for splitting and joining small links would be \$3 each; for large links it would be \$4 each.

How much should the man have to pay to have the endless chain made?

I got \$42. 2 large links together cost \$4 and there are 6 times that has to happen so those cost \$24. Also, on 6 occasions 2 small links go together, and at \$3 each, it costs \$18. 24+18=42

Edited by Gmaster479

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A man bought 12 lengths of chain, as shown, and asked the local blacksmith to forge them into an endless chain of 100 links.

The blacksmith said the cost for splitting and joining small links would be \$3 each; for large links it would be \$4 each.

How much should the man have to pay to have the endless chain made?

Meh...I'm probably wrong, but I say \$38

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A man bought 12 lengths of chain, as shown, and asked the local blacksmith to forge them into an endless chain of 100 links.

The blacksmith said the cost for splitting and joining small links would be \$3 each; for large links it would be \$4 each.

How much should the man have to pay to have the endless chain made?

Actually, sorry - Is it size of the link, not the quantity? I just noticed there are differences in the sizes of the rings...

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\$36. Need to split at 12 links to connect all the chains. Pay minimum for splitting only small links and joining to the large ones.

One way it can be done:

(starting at 12 o'clock and going clockwise, I numbered the chains 1 through 12)

take chain 3, split small end and join to chain 2. take chain 1 and split small end and join to other side of chain 2. Chain 4 has two small ends- split both, use to connect chains 9 and 1. chain 12 has two small ends- split both and use to connect chains 9 and large end of 10. Split small end of chain 10, connect to large end of 8. Split small end of chain 8 and connect to chain 6. Connect small end of chain 5 to other end of chain 6. Connect small end of 7 to large end of 5. Chain 11 has two small ends- split both, use to connect chains 7 and 3. Should complete the circle using all 12 chains and only splitting the small chains, thus minimizing the cost.

Is this right?

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\$36 .. there are 12 chains meaning there are 24 ends. There are 12 small links and 12 large links at the ends. Each join reduces the number of "ends" by 2 and you need to get down to no "ends" so 12 joins. You have 12 small chains you can cut so 12 * \$3 = 36.

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A man bought 12 lengths of chain, as shown, and asked the local blacksmith to forge them into an endless chain of 100 links.

The blacksmith said the cost for splitting and joining small links would be \$3 each; for large links it would be \$4 each.

How much should the man have to pay to have the endless chain made?

I get

Labeling the chains by the end links you can label them as SS, LL, or SL...we start with 3 SS, 3 LL, and 6 SL...you can connect each of the SS with the LLs for \$9...that leaves you with 9 SL remaining...you can then connect 4 sets of the SL together for \$12 and that leaves you with 5 SL remaining...connect another 2 sets of those for \$6, you have 3 SL remaining...connect one set of those for \$3, you have 2 SL remaining...connect those for another \$3...you now have one long SL left...so connect it for a final \$3...

total you spent \$36 plus the cost of the chain :c)

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I'm going with engspangussian as well. I just went with all the ends meeting as is on my answer and didn't think about saving money

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I can do it in \$34, not \$36.

There are two chains that have 5 links that go SBSBS (S is a small link and B is a big link). Simply cut all 10 of these links (5 in each chain). You are left with 10 cut and open links and 10 chains to attach in a circle. Use each cut link to attach two other chains together and you get your circle. The total cost is 6x\$3 + 4x\$4 = \$34.

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\$36. Where two small links face each other remove one and join two big ones. Then split the remaining small link and join it to the large link now across from it.

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I can do it in \$34, not \$36.

There are two chains that have 5 links that go SBSBS (S is a small link and B is a big link). Simply cut all 10 of these links (5 in each chain). You are left with 10 cut and open links and 10 chains to attach in a circle. Use each cut link to attach two other chains together and you get your circle. The total cost is 6x\$3 + 4x\$4 = \$34.

Does that give you a chain with 100 links in it?

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There are two 5-link chains containing 3 small and 2 big links.

As AI said, split all the links of these tow chains, and you get 10, cut open links. Now join the rest 10 chains by this.This way it costs only 34\$.

Don't start wondering why this time only 10 links works, this is because we have completely spilted two chains, removing the need to join them.

Edited by bonanova

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