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Chain Links

"one day a customer brought into the shop of abdul the jeweler six chains, each of which had five links. he wanted the six chains to be joined into one large circular chain and inquired as to the cost. 'well', replied the jeweler, 'every link i cut open and close costs one piece of silver.' .... how many pieces of silver are required for the job?"

disclaimer: i came up with a different answer than the one given in the book. granted, mine is a bit of a "backdoor" one, but i stand by it nonetheless.

submit your answer in the comments, and i'll confirm the correct one (and mine too). don't look at the comments unless you want to see the answer!

journeyfulloflaughter journeyfulloflaughter 26-30, F 31 Responses Dec 31, 2007

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The answer could be 5 as it would be the minimum possible number of cuts, I resind my previous post.

6 cuts for a large circle

Or u could cut all 5 links of 1 chain and use them to join the other 5 chains together

correct, indy.

I believe the answer is 5. If he cuts all 5 links of one of the chains, he can then use them to join the other 5 chains together.

actually, no. too many people touching me. ;)

5 is correct :)

......chew on unicorn??????

five is the correct answer. <br />
treefrogz, i didn't read it as "one piece of silver for every link opened, and an additional piece of silver for every link closed" just as "every link i cut open and close". but don't dwell too much on it.

that is, if you were referring to my cheapskate backdoor answer. i assumed you were. <br />
<br />
i have to go eat now, i'll come back for more headsplitting fun later ;)

but "open and close" means that if he only closed it, using his own silver, but didn't also cut it open, it doesn't apply.

getting rid of the 6th chain (by dividing up its 5 parts) means that only 5 chains remain to be closed. the 5 links from the 6th chain close the 5 remaining chains.<br />
<br />
or you can just refuse to pay anything, like me ;)

if you want to see the answers, they're on the previous page of comments. myspip got the correct one, and then i gave my "cheapskate" version ;)

no, lower than 12. myspip got it right, so avoid reading any of his comments ;)

lol, yeah today he'd probably have fine print ;)

Hahaha, cool :D You are indeed very intelligent :D<br />
Beware though, in a corrupt capitalistic system he'd charge you 1000000 gold coins for services that he himself did not mention ;)

mine is based on the wording of the jeweler. he said "every link i cut open and close costs 1 silver piece". my response would then be that he shouldn't cut open any of my links, instead he should use his own silver to craft new links joining all the chains. since he didn't cut any of mine, technically, i can't be charged. this is why businesses have to word their "offers" really carefully. because of people like me ;)

hehe sure :)<br />
5 seems obvious now :P there are some similar variants to get 5.<br />
<br />
But tell me yours!

exactly! 5 is the correct "book answer". you win!<br />
<br />
stop thinking about 4, that's not an answer at all!<br />
<br />
shall i reveal my "backdoor" way?

AH! I can reduce it to 5<br />
<br />
Cut open all five links of one chain, and let those be the joining points between the 5 remaining chains...<br />
<br />
Let me think how I can get to 4

lol, the "4" only told me to where to find the answer/explanation quickly in the book, instead of searching for it everytime! <br />
<br />
re: the parallel chains, no, they want it to be one big circle, like a traditional necklace.<br />
<br />
re: pigeonholes, you are way smarter than me. attempting to read it hurts my head.<br />
<br />
should i give the answers, or do you want to keep guessing?

4? hmm, I need you to explain that :P But let me think a bit more<br />
There must be a very smart and tricky way :P<br />
<br />
<br />
I was thinking, using conventional principles:<br />
<br />
if we have less than 6 cuts. then according to The Pidgeon Hole principle, at least one 5-linked chain has no cut link... Call one of these 5 linked-chains "A"<br />
For a circular large chain, then A is joined to 2 other 5-linked chains. THese two. call them B and F, must have been cut once each at the ends.<br />
The chains B and F are linked to C and E respectively... But the only way for these to link is through cutting once for each junction... <br />
<br />
After 4 cuts, we have the links E-F-A-B-C but E is not attached to C and D is not joined yet... so using this principle we get 6 cuts...

and for my own personal reference, this is problem number "4"

Sorry. I meant 2...<br />
<br />
You cut the ends of one chain... and join them with all the other 5 chains... THese five chains will be parallel. and thus it forms a circular chain of circumference 10 links

ooh, too much math! brain shutting down! <br />
the correct "book" answer is less than six.<br />
my "backdoor" answer is also less than six.<br />
neither is 3.<br />
and math hurts me ;)

I know 6 is possible, so the answer must be less than 6.<br />
<br />
But doesn't each juncture involve a cut?<br />
And we have 6 junctures (like the nodes of a hexagon)...<br />
<br />
Is the links like normal links we have in reality? <br />
<br />
Hmm, you didn't specify that the circular great-chain must be a simple graph.<br />
<br />
So a possibility would be 3,<br />
<br />
Let me elaborate...

6 is almost right, but still not quite.

I meant: <br />
Cut one link at the end of each chain and join it to an uncut link of end of the next chain...

6 is an obvious answer. cut one link of each chain and join in to the next chain...<br />
<br />
But perhaps that is not the least amount of money needed... Mathematically speaking there are different kinds of "Circular" chain... I assume you mean circular in the normal sense... like an "O"

:)