yaworsw/euler-manager

---
:id: 247
:name: Squares under a hyperbola
:url: https://projecteuler.net/problem=247
:content: "Consider the region constrained by 1 ≤ <var>x</var> and 0 ≤ <var>y</var>
  ≤ <sup>1</sup>/<sub><var>x</var></sub>.\n\nLet S<sub>1</sub> be the largest square
  that can fit under the curve.  \nLet S<sub>2</sub> be the largest square that fits
  in the remaining area, and so on.   \nLet the _index_ of S<sub><var>n</var></sub>
  be the pair (left, below) indicating the number of squares to the left of S<sub><var>n</var></sub>
  and the number of squares below S<sub><var>n</var></sub>.\n\n ![]({{ images_dir
  }}/p247_hypersquares.gif)\n\nThe diagram shows some such squares labelled by number.
  \  \nS<sub>2</sub> has one square to its left and none below, so the index of S<sub>2</sub>
  is (1,0).  \nIt can be seen that the index of S<sub>32</sub> is (1,1) as is the
  index of S<sub>50</sub>.   \n50 is the largest <var>n</var> for which the index
  of S<sub><var>n</var></sub> is (1,1).\n\nWhat is the largest <var>n</var> for which
  the index of S<sub><var>n</var></sub> is (3,3)?\n\n"