yaworsw/euler-manager

---
:id: 86
:name: Cuboid route
:url: https://projecteuler.net/problem=86
:content: "A spider, S, sits in one corner of a cuboid room, measuring 6 by 5 by 3,
  and a fly, F, sits in the opposite corner. By travelling on the surfaces of the
  room the shortest \"straight line\" distance from S to F is 10 and the path is shown
  on the diagram.\n\n ![]({{ images_dir }}/p086.gif)  \n\nHowever, there are up to
  three \"shortest\" path candidates for any given cuboid and the shortest route doesn't
  always have integer length.\n\nIt can be shown that there are exactly 2060 distinct
  cuboids, ignoring rotations, with integer dimensions, up to a maximum size of M
  by M by M, for which the shortest route has integer length when M = 100. This is
  the least value of M for which the number of solutions first exceeds two thousand;
  the number of solutions when M = 99 is 1975.\n\nFind the least value of M such that
  the number of solutions first exceeds one million.\n\n"