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Enigmas & puzzles

Cutting the links

By Ian Stewart   June 2009

“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…

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