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March 26th, 2014, 09:42 PM  #1 
Senior Member Joined: Oct 2013 From: Far far away Posts: 429 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  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: The 5 chain problem Hello, shunya! Quote:
Your second solution is correct (obviously). In general, your procedure will work [color=beige]. . [/color]for chains, each with 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:
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 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Quote:
Cutting Links  Puzzles And Riddles  

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