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Join six five-link chains to form a circular chain.
To join two chains, you must cut, and then re-weld, a link.

The final number of links in the circular chain will be 30.

What is the minimum number of links you must cut and re-weld to complete the circle/chain?

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Think of each of the five-link chains as a line of hoops or rings that are connected end to end. – Olive Stemforn Mar 23 at 17:59
    
I'm pretty sure I've seen this before... (Also, logic-puzzle should only be used for puzzles about logical deduction.) – Deusovi Mar 23 at 18:19
    
(Not entirely sure if topology applies here.) – Deusovi Mar 23 at 18:20
    
@Deusovi Topology seems like a ... not-unreasonable tag to me? – question_asker Mar 23 at 18:20
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@OliveStemforn Click the green checkmark beside the answer that you said solved it correctly. – OldBunny2800 Mar 23 at 20:07
up vote 15 down vote accepted

5 Links. Cut one of the segments into separate links,(5 cuts) and use them between each of the 5 remaining segments to form a circle (5 welds)

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Edit: The question was changed to stipulate that the chain should become a circle of 30 links in length. While this "solution" is a circle with 30 links, it is only 10 links long and is no longer valid after the update.

As is usual with these puzzles, I'm not sure if this is allowed:

Cut both ends of the first chain
Line up one side of the links of the other 5 chains
Weld the broken link through all 5 whole links.
repeat for the other side
You should now have a "circle" of 10 links around, that has a fat one side (5 chains thick!)
This means that the answer is 2 cuts. See Images.

Just leave a comment if you need clarification.

Step one Step two

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In that case you can do it with one cut. Cut one link in one chain, gather up the other links of that chain in the cut link, and then also gather up the two end links from all the other chains. You'll have a circular chain that's five chains wide, with a funny fat link connecting the two ends. – Mike Scott Mar 23 at 19:57
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I thought about that, but then you'd have a "tail" on the end. While useful for beating your opponents, somewhat contrary to a circle. – goodguy5 Mar 23 at 19:59

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