perplexus.info :: General : A chain in payment

A chain in payment (Posted on 2002-05-04)

You must use a gold chain to pay a worker for seven days of service. The chain has seven links on it, and you agree on a price of one link per day.

However, the worker will not work without getting the day's pay up front, and you do not wish to give him more than his due for the fear that he will take it and leave. Therefore, you realised that you must cut some of the links on the chain.

What is the smallest number of links you will need to cut, so that you can make sure that the worker receives one link for every day that he works, but not more?

Submitted by levik

Rating: 3.0000 (9 votes)

Solution: (Hide)

The answer to this problem is "one link". This might be surprising to people who have heard a similar problem where the payment was a bar of gold, rather than a chain.
By cutting the third link of a chain open, you end up with the one broken link, a two-link piece of chain on its left, and a four-link piece on its right.
Then make the payments as follows:

Give the one link. (1)
Give 2 links, take back 1 (1+2-1=2)
Give one link back. (2+1=3)
Give 4 links, take back 2 and 1 (3+4-2-1=4)
Give 1 (4+1=5)
Give 2, take 1 (5+2-1=6)
Give 1 (6+1=7)
The difference from the problem with the gold bar is that by cutting one link, you make 3 pieces of the chain, instead of 2.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
answer	K Sengupta	2007-04-01 15:15:40
spend-happy worker	Jack Squat	2003-12-10 09:06:15
please ignore	FatBoy	2003-09-11 12:03:01
Good Twist	cges	2002-12-11 08:28:44
No Subject	James	2002-11-16 19:12:46
Hm...	suna	2002-11-12 09:34:35
Hire a new worker	Mike	2002-05-10 15:34:49
Revision of solution	Fizzle	2002-05-08 13:15:02
Solution	Govind	2002-05-05 07:43:52

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