## Thursday, May 20, 2010

### A Chain Loan

Greek Government recently got a \$140 billion aid package from the International Monetary Fund. Imagine that International Monetary Fund would like to get some symbolic collateral for the loan and is eying an ancient gold link chain (believed to belong to Aphrodite) from the Athens's Museum. The chain has only seven links, all connected in a row. Monetary Fund wants one link for each year until the loan is returned. Meaning that it wants to hold to one ring in the first year of the loan, two rings in the second, three in the third etc. Greek government agrees but demands that chain be minimally damaged and only one link out of the whole chain be cut. Is that possible?

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Wang said...

The question doesn't say how many years until the loan is returned.

Assuming they wanted a link for all 7 years (for the 7 links) I doubt that its possible with only one link cut.

It is possible however, with 2 link cuts:

Give the monetary fund 1 link in the first year.
Give the monetary fund the 2 links in the second year, take back the 1 link.
Give the monetary fund the 1 link in the third year.
Give the monetary fund the 4 links in the fourth year and take back the 1 and 2 links.
Give the monetary fund the 1 link in the fifth year.
Give the monetary fund the 2 links in the sixth year, taking back the 1 link.

Finally, give the monetary fund the 1 link in the seventh year, thus the monetary fund has all seven links.

Maria said...

You are absolutely right!
If you count two links and then cut the third and take it away by pushing cut sides away from each other, you will end up with three pieces: 2 links long, 1 link long and 4 links long. From these links you could create all the combination from 1 to 7!