### Due October 18th

This problem can be solved with logic. We consider this to be a Hard problem, worth 20 points. Send answers and questions to mathstat@uoguelph.ca

A traveler in Africa wants to stay at an inn for a week. The innkeeper does not trust his own government's currency and cannot accept foreign money. He demands payment in some form he can use to trade. The traveler has a silver chain with seven links that he brought for just such an occasion. If a link is cut it can be taken out of the chain so that the chain on either side of it forms two smaller chains. The traveler and the innkeeper agree on a price of one link per day, to be paid at the start of each day. The innkeeper also wants as few links cut as possible because uncut pieces of the chain are easier to trade. What is the smallest number of links that need to be cut to permit the traveler to keep his payment current? This means that on first day the innkeeper should have one link and the traveler should have six, on the second day the innkeeper should have two links and the traveler should have five, and so on.

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