Chain Reaction Puzzle - Solution

The Puzzle:

Chain Reaction
Chains. Make-up. What's the connection? The answer lies in a film. The DIY chain of shops, TEXAS, once made a film about their new eye make-up. They called it "The Texas Chain Store Mascara". I digress.

Below you can see several bits of broken chain. I have been told to join up all the pieces to make a complete necklace using all twenty links.

However, it is a very fiddly job, and it takes one minute to cut one link, and two minutes to join it up again. How long will it take me to finish the necklace?

Our Solution:

Just 15 minutes!! That's a surprise, isn't it? I'm sure you're on the very edge of your seat to know how it's done.

I'll tell you anyway.

Separate the two shortest lengths of chain by two cuts. This makes two open links and four single closed ones.
Time taken: 2 minutes.
Cut open three of the single links. This leaves five open links and five pieces of chain (4, 4, 3, 3, 1).
Time taken: 3 minutes.
Use the five open links to join the five pieces of chain (each link joins two ends).
Time taken: 10 minutes.


Puzzle Author: Stephen Froggatt

See this puzzle without solution
Discuss this puzzle at the Math is Fun Forum