My Math Forum The 5 chain problem

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March 27th, 2014, 07:33 AM   #2
Math Team

Joined: Dec 2006
From: Lexington, MA

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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

Joined: Oct 2011

Posts: 14,597
Thanks: 1038

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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# six chain four link problem

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