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curriculum/challenges/italian/10-coding-interview-prep/project-euler/problem-309-integer-ladders.md

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+---
+id: 5900f4a11000cf542c50ffb4
+title: 'Problem 309: Integer Ladders'
+challengeType: 5
+forumTopicId: 301963
+dashedName: 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).
+
+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--
+
+`euler309()` should return 210139.
+
+```js
+assert.strictEqual(euler309(), 210139);
+```
+
+# --seed--
+
+## --seed-contents--
+
+```js
+function euler309() {
+
+  return true;
+}
+
+euler309();
+```
+
+# --solutions--
+
+```js
+// solution required
+```