Project Euler/247

Problem Statement

Squares Under a Hyperbola

Consider the region constrained by 1 ≤ x and 0 ≤ y ≤ 1/x.

Let S_1 be the largest square that can fit entirely within this region, touching the curve at one point.

Let S_2 be the largest square that fits in the remaining area, and so on.

Let the index of S_n be the ordered pair (left, below) indicating how many squares touch S_n on its left side and how many squares touch S_n on its bottom side.

What is the index of the square containing (3,3)?

Find the index (a,b) of the largest such square, and give a+b.