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Topic: GOLD CHAIN (Read 6882 times) |
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drdedos
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"a man has a gold chain with 7 links. he needs the service of a laborer for 7 days at a fee of one gold link per day. however, each day of work needs to be paid for separately. in other words, the worker must be paid each day after working and if the laborer is ever overpaid he will quit with the extra money. also he will never allow himself to be owed a link. what is the fewest number of cuts to the chain to facilitate this arrangement and how does that guarantee payment?"
Cut the chain twice from "OOOOOOO" to "O OO OOOO"
Day 1: Give single link => O
Day 2: Take back single link and give double link => OO
Day 3: Give single link again => O OO
Day 4: Take back all links and give quadruple link => OOOO
Day 5: Give single link again => O OOOO
Day 6: Take back single link and give double link => OO OOOO
Day 7: Give it all up => O OO OOOO
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S. Owen
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Posts: 221
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Re: GOLD CHAIN
« Reply #1 on: Jul 29th, 2002, 8:32pm » |
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I think that interpreting the problem to allow for "making change" is fine, and I like this solution.
You can do it with just one cut though - cut link #3. This gives you one cut link, and two pieces consisting of two links and four links.
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drdedos
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"You can do it with just one cut though - cut link #3."
Cutting out link #3 still requires two cuts, one before the link and one after it.
OOOOOOO => OO (cut) O (cut) OOOO
I think this is no different from my solution:
OOOOOOO => O (cut) OO (cut) OOOO
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Alex
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I think you're assuming the links are connected by some medium that can be severed without breaking the links themselves. If you cut the 3rd link open, you use that link as the single, pull the first two off the 3rd link as a pair, and the last 4 as the set of four.
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chaz
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Gold is very malleable. So you could easily cut link #3, twist or stretch it open, and remove the other two sections.
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BoredAtWork
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What if we can't make change? I took the riddle to mean that you gave him one link from the chain per day. I don't know that it is necessarily reasonable to assume that the laborer brings the old links of chain back and offers it back to the boss in exchange for a new set of links. Instead, I think that you would need to work under the assumption that once a particular link is out of your control - in the hands of the laborer - that it will no longer be an option for consideration.
With this in mind ....
You have 7 links labeled 1 through 7 ( 1234567 ).
Day one - Cut link 2. This frees link 1 and link 2, so that the first day you can give the laborer link 1. ( 2 34567 ) ( 1 )
Day two - Give the laborer link 2 which was freed the previous day. ( 34567 ) ( 12 )
Day three - Cut link 4. This frees link 4 and link 3. Give link 3 to the laborer. ( 4 567 ) ( 123 )
Day four - Give the laborer link 4 which was freed the previous day. ( 567 ) ( 1234 )
Day five - Cut link 6. You now have 3 separate links ( 5,6 and 7 ) which may be used to pay for today and the next 2 days separately.
So, you make 3 cuts to the chain, and can pay the laborer 1 link per day.
Let me know what you think.
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loucura
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One cut.
You have chain 0000000, cust straight through the center of the chain, through -all- enjoining links. You now have half-links UUUUUUU = uuuuuuu
Give the worker a U and a u halflink every day, he's paid 1 link, and you won't overpay.
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wowbagger
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Re: GOLD CHAIN
« Reply #7 on: Aug 25th, 2002, 8:04am » |
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First of all, I think a solution requiring the labourer giving change is disallowed by the following statements:
"[...] if the laborer is ever overpaid he will quit with the extra money.
also he will never allow himself to be owed a link."
The first part implies that once you give him two links (on the second day) he'll quit before giving the change. The latter part states that he will not give you the one link he got the first day in advance of the two links.
Hmm, maybe one could arrange for a simultaneous exchange?
on Aug 22nd, 2002, 1:59pm, loucura wrote:One cut.
You have chain 0000000, cust straight through the center of the chain, through -all- enjoining links. You now have half-links UUUUUUU = uuuuuuu
Give the worker a U and a u halflink every day, he's paid 1 link, and you won't overpay.
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If that is allowed to be counted as "one cut", you can also arrive at seven loose links by cutting links 2, 4, and 6 as proposed by BoredAtWork in "one cut":
O O O O cut through top parts
O O O <-- of links standing upright
This way you'd avoid paying two half-links (just in case that's bugging anyone).
Anyway, a crafty solution, and very probably the minimum number of cuts - unless the "chain" consisted of open links to start with.
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