"I have nine separate pieces of gold chain," said Esmeralda to the jeweller, "and I want to make one necklace from them."
The jeweller picked up one of the chains that Esmerelda placed on his counter.
"That's the longest—it's eight links," said Esmeralda helpfully. "There are three that are five links long and two that are six. The others are seven, four and three links long."
"It costs £2 to cut each link of chain," the jeweller said, "and £4 to rejoin it."
"So how expensive will it be?"
"If I cut the links at the ends of each piece and link the chains one a time then I'd have to cut and rejoin a link nine times—so the total cost would be £54. But I could sell you a gold chain for £50."
"Isn't there another way to do it?"
The jeweller scratched his head. "I could break each link on the longest chain. Then I could use them to join the remaining pieces together. That would cost £48."
"That's still more than I want to spend."
"I could leave out some of the chains, or some of the links—"
"No, I want to use all the links, and all the lengths of chain. And I'm sure that there's a better way to do it."
What is the cheapest method to use?
Prospect invites you to solve the puzzle and send us the solution. Correct answers will be entered into a draw. The winner will receive a copy of In Search of Time: Journeys Along a Curious Dimension by Dan Falk (National Maritime Museum, £14.99). Send your solution to answer@prospect-magazine.co.uk by 12th June.
The winner will be announced in our July issue. Last month's winner was Hannah Joseph, London SW12
Last month's answer
Aside from rotations and reflections, there is only one way to arrange the flowerpots.
