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id	title	challengeType	forumTopicId	dashedName
5900f4a11000cf542c50ffb4	Problem 309: Integer Ladders	5	301963	problem-309-integer-ladders

--description--

In the classic "Crossing Ladders" problem, we are given the lengths x and y of two ladders resting on the opposite walls of a narrow, level street. We are also given the height h above the street where the two ladders cross and we are asked to find the width of the street (w).

ladders x and y, crossing at the height h, and resting on opposite walls of the street of width w

Here, we are only concerned with instances where all four variables are positive integers. For example, if x = 70, y = 119 and h = 30, we can calculate that w = 56.

In fact, for integer values x, y, h and 0 < x < y < 200, there are only five triplets (x, y, h) producing integer solutions for w: (70, 119, 30), (74, 182, 21), (87, 105, 35), (100, 116, 35) and (119, 175, 40).

For integer values x, y, h and 0 < x < y < 1\\,000\\,000, how many triplets (x, y, h) produce integer solutions for w?

--hints--

integerLadders() should return 210139.

assert.strictEqual(integerLadders(), 210139);

--seed--

--seed-contents--

function integerLadders() {

  return true;
}

integerLadders();

--solutions--

// solution required

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