45 lines
1.2 KiB
Markdown
45 lines
1.2 KiB
Markdown
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---
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id: 5900f4a11000cf542c50ffb4
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title: 'Problem 309: Integer Ladders'
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challengeType: 5
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forumTopicId: 301963
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dashedName: problem-309-integer-ladders
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---
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# --description--
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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).
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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.
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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).
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For integer values x, y, h and 0 < x < y < 1 000 000, how many triplets (x,y,h) produce integer solutions for w?
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# --hints--
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`euler309()` should return 210139.
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```js
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assert.strictEqual(euler309(), 210139);
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```
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# --seed--
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## --seed-contents--
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```js
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function euler309() {
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return true;
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}
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euler309();
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```
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# --solutions--
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```js
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// solution required
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```
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