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Challenge 252: Gainful Gardening

I have a silver chain with 31 individual links in it, and I am going to use it to pay a gardener to work in my garden every day in March, at a rate of one link per day. However, it is expensive to get a jeweller to cut up the chain – he charges a fixed amount per cut.

I can avoid cutting the chain into 31 separate links, however, by giving the gardener parts of the chain I still have, in exchange for some I have already given her.

For instance, if I had two individual links and a chain of three I could cover the first five days by:

  • on day one, giving her one link;
  • on day two, giving her a second link;
  • on day three, taking back the first two links, and giving her the chain of three;
  • on day four giving her one link (which I now have back)
  • on day five, giving her one link.

What lengths should I get the jeweller to cut the chain into so that I can make sure that my gardener has been paid the right amount at the end of every day in March, but pay as little as possible for the cutting?

Could you get away with fewer cuts in February?

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