yaworsw/euler-manager

---
:id: 242
:name: Odd Triplets
:url: https://projecteuler.net/problem=242
:content: "Given the set {1,2,...,<var>n</var>}, we define <var>f</var>(<var>n</var>,<var>k</var>)
  as the number of its <var>k</var>-element subsets with an odd sum of elements. For
  example, <var>f</var>(5,3) = 4, since the set {1,2,3,4,5} has four 3-element subsets
  having an odd sum of elements, i.e.: {1,2,4}, {1,3,5}, {2,3,4} and {2,4,5}.\n\nWhen
  all three values <var>n</var>, <var>k</var> and <var>f</var>(<var>n</var>,<var>k</var>)
  are odd, we say that they make   \nan _odd-triplet_ [<var>n</var>,<var>k</var>,<var>f</var>(<var>n</var>,<var>k</var>)].\n\nThere
  are exactly five odd-triplets with <var>n</var> ≤ 10, namely:  \n[1,1,<var>f</var>(1,1) = 1],
  [5,1,<var>f</var>(5,1) = 3], [5,5,<var>f</var>(5,5) = 1], [9,1,<var>f</var>(9,1) = 5]
  and [9,9,<var>f</var>(9,9) = 1].\n\nHow many odd-triplets are there with <var>n</var> ≤ 10<sup>12</sup> ?\n\n"