The Bling Chain Problem

You’re looking through your friend’s jewellery drawer when you find a glorious selection of broken chains. There are a total of 5 short chains in there and each one has 4 gold links.

You ask your friend about the chains and they say you’re free to keep them if you can make them into a complete necklace. You gladly accept the offer.

A jeweller tells you that the cost of reforging this necklace will be £10 for each link they have to break and reseal.

In light of this, how much will it cost to rebuild the necklace, and what’s the cheapest price you can negotiate?

The simplest solution is breaking one link on all 5 chains and attaching them together. This would cost £50 in total.

However, the cheapest way is to take one of the chains (which has 4 links) and break all 4 links.

This leaves you with 4 links:

Chain A connects to chain B: 1 link.

Chain B connects to chain C: 1 link.

Chain C connects to chain D: 1 link.

Chain D connects to chain E: 1 link.

You’re only breaking 4 links here instead of 5, which costs £40 – a saving of £10!

Go and spend it on something nice and enjoy your free necklace!


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