Cutting a gold chain to pay rent

Question

You have a gold chain of 7 links and owe a hotel one link per day for 7 days. The hotel insists on being paid exactly one link's worth each day (no prepaying more than you owe), but it will make change, it can hold links you've given and hand some back. You want to disturb the chain as little as possible. What is the minimum number of cuts, and how do you make the daily payments?

Accepted Answer

The answer is one cut. The cut. Cut open the 3rd link of the chain. Cutting a single link frees that one link and splits the remainder, leaving three pieces: - a single 1-link piece (the opened link), - a 2-link piece, and - a 4-link piece. (The links before the cut form a 2-chain, the links after form a 4-chain, and the cut link itself is the 1.) Daily payments (give = hand to hotel, take = receive change): Day Action Hotel holds ------------------------------------------------ 1 give the 1 1 2 give the 2, take back the 1 2 3 give the 1 3 4 give the 4, take back the 1 and 2 4 5 give the 1 5 …

Cutting a gold chain to pay rent

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