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 3 x 5 = 15 cents. Use these open links to connect the other lengths of chain. This costs 3 x 10 = 30 cents. Total cost is only 45 cents.