Puzzle 115 - solution

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 The traveler cuts the third link.

  • On the first day, he pays this cut link.
  • Second day, he pays two links and gets back one cut link. 
  • Third day, he pays three links and gets back two links.
  • Fourth day, he pays cut link again.
  • Fifth day, he pays two links and gets back cut link.
  • Sixth day, he pays the cut link again. 
 

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