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 March 26th, 2014, 09:42 PM #1 Senior Member     Joined: Oct 2013 From: Far far away Posts: 422 Thanks: 18 The 5 chain problem Question: Suppose that you have 5 chains each consisting of 3 links. If a single chain of 15 links is to be formed by cutting and welding, what is the fewest number of cuts that need to be made? My attempt 1) There are 5 chains (each with 3 links). So we require 4 joints between them. So we need to cut & weld 4 links. Therefore the fewest number of cuts is 4 My attempt 2) There are 5 chains (each with 3 links). We take one chain and cut all three links. Now we are left with only 4 chains. This requires only 3 joints. Exactly the number of links I have. Therefore, the fewest number of cuts is 3 My second answer seems right. Am I correct? Also is there something mathematical about this problem? If there is, I'm not getting it. Thanks
March 27th, 2014, 07:33 AM   #2
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Re: The 5 chain problem

Hello, shunya!

Quote:
 Suppose that you have 5 chains each consisting of 3 links. If a single chain of 15 links is to be formed by cutting and welding, what is the fewest number of cuts that need to be made?

Your second solution is correct (obviously).

In general, your procedure will work
[color=beige]. . [/color]for $n+2$ chains, each with $n$ links.

Example: 8 chains, each with 6 links.
[color=beige]. . [/color]Open the 6 links on one chain.
[color=beige]. . [/color]Use them to join the other 7 chains.

There is a popular variation of this problem.

Quote:
 Suppose that you have 5 chains each consisting of 4 links. If a necklace of 20 links is to be formed by cutting and welding, what is the fewest number of cuts that need to be made?

Solution: Open the 4 links on one chain.
[color=beige]. . . . . . .[/color]Use them to join the other 4 chains.

Last edited by soroban; March 28th, 2014 at 03:22 PM.

 October 11th, 2015, 10:49 PM #3 Newbie   Joined: Oct 2015 From: Adeliade Posts: 1 Thanks: 0 I don't get this. Isn't the chain meant to be in one line?? Can someone diagram or explain it simpler plzzzz.
October 14th, 2015, 07:26 AM   #4
Math Team

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From: Ottawa Ontario, Canada

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Quote:
 Originally Posted by stucker41 I don't get this. Isn't the chain meant to be in one line?? Can someone diagram or explain it simpler plzzzz.
This is an old well-known puzzle; go here :
Cutting Links - Puzzles And Riddles

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