4 Pages

Extension of the Chain-Cutting Problem

An ancient problem concerning chain-cutting appears in various dresses [2, p. 276;3, pp. 29;33;4, p. 51], among them the following:

A traveler has a gold chain with seven links. He agrees to pay his rent at the rate of one link per day with the understanding that he may redeem them if his business venture is successful. He must pay his rent daily, but wishes to keep the chain as nearly intact as possible. What is the fewest number of cuts he must make in the chain?