The Gold Chain Puzzle
You have fragments of a gold chain which you would like joined together so as to make a continuous chain. These are the nine pieces and this is the final chain you hope to have made.
When you visit the jeweller, she says that you could buy a chain very similar in size and weight for £85. If you would prefer to remake your original chain, the goldsmith charges £10 for each link cut and resoldered to join to the next link.
The puzzle is to work out the cheapest price to get a complete gold chain?
The answer is £70 but how did you work this out?
To begin, the simplest way to remake the original chain is to cut one link of each piece and rejoin all the pieces. Now this would means nine cut-and-resolder operations which would cost you £90. So buying a new chain would be cheaper.
There are other ideas.
Suppose the goldsmith cuts all the eight links in the longest piece and uses them to connect all the remaining pieces. That would be eight cut-and-resolder operations which would only cost £80. However you are still paying more than you need to. Let’s keep going.
The picture shows you the final answer. If the goldsmith cuts up the 3-link piece and a 4-link piece he will have enough links to connect all the other pieces in a complete circle. For £70 you have a bargain!
