id	title	challengeType	forumTopicId	dashedName
5900f4641000cf542c50ff76	Problem 247: Squares under a hyperbola	5	301894	problem-247-squares-under-a-hyperbola

--description--

Consider the region constrained by 1 ≤ x and 0 ≤ y ≤ \frac{1}{x}.

Let S_1 be the largest square that can fit under the curve.

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

Let the index of S_n be the pair (left, below) indicating the number of squares to the left of S_n and the number of squares below S_n.

The diagram shows some such squares labelled by number.

S_2 has one square to its left and none below, so the index of S_2 is (1, 0).

It can be seen that the index of S_{32} is (1,1) as is the index of S_{50}.

50 is the largest n for which the index of S_n is (1, 1).

What is the largest n for which the index of S_n is (3, 3)?

--hints--

squaresUnderAHyperbola() should return 782252.

assert.strictEqual(squaresUnderAHyperbola(), 782252);

function squaresUnderAHyperbola() {

  return true;
}

squaresUnderAHyperbola();

// solution required