47 lines
1.5 KiB
Markdown
47 lines
1.5 KiB
Markdown
---
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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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<img class="img-responsive center-block" alt="ladders x and y, crossing at the height h, and resting on opposite walls of the street of width w" src="https://cdn.freecodecamp.org/curriculum/project-euler/integer-ladders.gif" style="background-color: white; padding: 10px;">
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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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`integerLadders()` should return `210139`.
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```js
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assert.strictEqual(integerLadders(), 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 integerLadders() {
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return true;
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}
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integerLadders();
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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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