Here are five lenths of chain, three links apiece. To break a chain costs 5 cents; to weld a link closed again costs 10 cents. How cheaply can one weld these 5 pieces into a single chain of 15 links? Explain how to do it.
Solution
Take one chain completely apart giving three single open links. This costs cents. Use these open links to connect the other lengths of chain. This costs cents. Total cost is only 45 cents.