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# A simple gold link puzzle

## Question

A man needed to pay his rent and was out of money, but found that his rent was worth about one gold link on his chain per day. What is the fewest number of cuts he can make in his 23-link chain to pay the rent for up to 23 days?

## 10 answers to this question

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Zero, just give him the chain at the end of 23 days.

But if you have to pay at the end of each day then 3 would be minimum Cut links 2, 6 and 14.

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Zero, just give him the chain at the end of 23 days.

But if you have to pay at the end of each day then 3 would be minimum Cut links 2, 6 and 14.

Thanks for pointing it out.... Read below the correct puzzle:

A man needs to pay his rent daily and was out of money, but found that his rent was worth about one gold link on his chain per day. What is the fewest number of cuts he can make in his 23-link chain to pay the rent for up to 23 days?

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4 if chain is in ring, 3 if not attached at either end

8|8|4|2|1[|]

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Zero, just give him the chain at the end of 23 days.

But if you have to pay at the end of each day then 3 would be minimum Cut links 2, 6 and 14.

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4 if chain is in ring, 3 if not attached at either end

8|8|4|2|1[|]

Chain is not connected at ends, i.e. it is not a circular but linear chain... you are close to correct answer...

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You can do it with two cuts: links 4 and 11.

You'd have lengths of 1, 1, 3, 6 and 12.

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Example of a Chain with links...

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Two cuts:4, 11

First cut anywhere on the chain would give us one link plus two groups of links.

That will not be enough, so a second cut is need, this will then give us two single links and three groups of link.

Since we can pay for two days with the single links, we would need a three link one for the third day. (receiving back the two single links.)

These then can pay for day four and five.

So we would then need a six link to pay for day six.

Days 7 - 11 can be paid for.

To pay for day 12 then we need 12 links with is the size of the peice remaining.

So each day after that can be paid for in the peice already cut.

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If one link is attached to another & it is linear chain, one link per day is to be paid then Minimum 11 cuts will be required.

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