You want to stay at an inn for seven nights. It costs one gold ring per night. You have exactly seven gold rings, so you show them to the innkeeper. However, your rings are all chained to each other in a straight line (not a circular chain). You want to pay the innkeeper the whole chain to stay for seven nights, but he doesn’t want to be in debt to you. Then, you tell the innkeeper that you will pay the whole bill on the last day, but the innkeeper says that he doesn’t want you to owe him either. You decide to cut all rings to pay him one per night, but the innkeeper doesn’t want cut rings. You think hard on how to pay him because you really need to stay at that inn. The innkeeper says, “okay fine, I will accept one cut ring, but just one. All the others must be full gold rings.” How can you pay the innkeeper, satisfying all his wants?
August 9th, 2011 | Category: 
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Cut the 3rd ring in the chain, you’ll end up with 3 parts: 1 Ring, 2 Rings, and 4 rings
With these 3 parts you can cover all possibilities between 1 and 7 without either one of you ever being in debt.
You are correct, Rool!
Cut the third ring, leaving you with groups of 1, 2 and 4 rings. This is easy to combine into any number from 1 to 7: On the first day, give 1; on the second day, take that back and give the chain of 2; on the third day, let him keep the 2 and add the 1 as well; on the fourth day, take back both give him the chain of 4; etc.
You’re today’s winner.
cut the 3rd ring in, from one end.
give the cut ring the first day.
Exchange that for the 2 rings the second day.
Give the cut ring the 3rd day.
Exchange the 4 connected rings for the cut ring and 2 connected rings on the forth day.
Give the cut ring on the 5th day.
Exchange the cut ring for the 2 connected ring on the 6th day.
Give the cut ring on the 7th day.