[Guest]

You want to stay in an inn for seven nights. It costs one gold piece per night. You have exactly seven gold rings, so you show them to the innkeeper. He says that he would allow you to pay in gold rings instead of gold pieces; however, your rings are all chained to each other in a straight line (not 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 someone. Then, you tell the innkeeper that you decide to pay it on the last day, but the innkeeper says that he doesn't want someone else 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 so hard on how to pay him because you really need to stay in 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 could you pay the innkeeper satisfying his wants?

[Guest]

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.

(Note: Because 1, 2 and 4 are powers of 2, in effect you're simply counting in binary)

[Guest]

Just cut a straight line cut through all the rings.

[Guest]

you cut the third ring in, so you have one cut ring one link of two and one link of four

The first night you give the innkeeper the cut ring

The second night you get the cut ring back and give the innkeeper a link of two rings

The third night you give the innkeeper the cut ring

The fourth night you get the the linked and cut rings back and give the inkeeper the link of four rings

the fifth night you give the inkeeper the cut ring

the sixth night you get the cut ring back and give the innkeeper the link of two rings

the last night you give the inkeeper the cut ring and the entire stay is paid for.

[Guest]

cut 3rd ring..it will give you 3 parts (1,2) 3 (4,5,6,7)...its easy...even inkeeper will take and give rings as per his requirement if you offer these 3 links to him..

Edited March 26, 2011 by Panwar

[Guest]

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.

(Note: Because 1, 2 and 4 are powers of 2, in effect you're simply counting in binary)

Nicely done, Gihan.

[Guest]

The answer is that you cut the 3rd ring. So, it would result to three chains: the third cut ring, the first to second rings chain, and the fourth to seventh rings chain. You now have a chain of these number of rings: 1, 2 and 4 rings (You are counting in binary numbers, as explained by Gihan.)

On the first night, give the chain with 1 ring. [That gives 1 ring]

On the second night, give the chain with 2 rings; then, get the chain with 1 ring back from him. [That gives 2 rings]

On the third night, give the chain with 1 ring (in addition to the 2 rings you already paid) [That gives 3 rings]

On the fourth night, give the chain with 4 rings; then, get the chains with 1 ring, and 2 rings back from him. [That gives 4 rings]

On the fifth night, give the chain with 1 ring (in addition to the chain with 4 rings you already paid) [That gives 5 rings]

On the sixth night, give the chain with 2 rings (in addition to the chain with 4 rings you already paid); then, get the chain with 1 ring back from him. [That gives 6 rings]

On the seventh night, give the chain with 1 ring (in addition to the chain with 4 rings and the chain with 2 rings you already paid) [That gives 7 rings]

That's it!

Congrats to the following who got the correct answer: Gihan, generalsolve, Panwar.

Thanks for saying my puzzle's cool, Gihan!

Welcome to the Den, generalsolve!

As for thlancaster, sorry but your answer is wrong. If you cut a straight line through all rings, then all 7 rings will be cut, but the innkeeper only allows you to cut one ring. Welcome to the Den, by the way, thlancaster!

Edited March 27, 2011 by Perry the Platypus