# Chain Quiz Puzzle

This puzzle requires a little bit of thought, but has a satisfyingly neat solution.

Whilst sorting through some old jewellery a colleague of ours discovered seven pieces of a chain in different lengths. The seven pieces were two, three, four, five, six, seven and eight links long, making a total of 35 links.

It was a lovely chain, and she decided to have the pieces joined together so that she could wear it as a piece of jewellery. And so she sought the services of a jeweller to do the work.

She was disappointed to discover that the jeweller would charge £17.50 to join up the pieces, and asked for a breakdown of the charges. The jeweller said that it cost 50p to cut a link and £2.00 to weld the link back together. There were seven pieces, and so it required seven cuts and seven welds to make a continuous loop of chain. Seven lots of £2.50 comes to £17.50, the price the jeweller was quoting.

Is this the cheapest solution? And if not, what is the cheapest way to make the chain complete?