85 lines
2.0 KiB
Markdown
85 lines
2.0 KiB
Markdown
---
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id: 5900f3ca1000cf542c50fedd
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title: 'Problem 94: Almost equilateral triangles'
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challengeType: 5
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forumTopicId: 302211
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dashedName: problem-94-almost-equilateral-triangles
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---
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# --description--
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It is easily proved that no equilateral triangle exists with integral length sides and integral area. However, the almost equilateral triangle 5-5-6 has an area of 12 square units.
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We shall define an <dfn>almost equilateral triangle</dfn> to be a triangle for which two sides are equal and the third differs by no more than one unit.
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Find the sum of the perimeters of all almost equilateral triangles with integral side lengths and area and whose perimeters do not exceed `limit`.
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# --hints--
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`almostEquilateralTriangles(50)` should return a number.
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```js
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assert(typeof almostEquilateralTriangles(50) === 'number');
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```
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`almostEquilateralTriangles(50)` should return `66`.
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```js
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assert.strictEqual(almostEquilateralTriangles(50), 66);
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```
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`almostEquilateralTriangles(10000)` should return `3688`.
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```js
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assert.strictEqual(almostEquilateralTriangles(10000), 3688);
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```
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`almostEquilateralTriangles(10000000)` should return `9973078`.
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```js
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assert.strictEqual(almostEquilateralTriangles(10000000), 9973078);
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```
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`almostEquilateralTriangles(1000000000)` should return `518408346`.
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```js
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assert.strictEqual(almostEquilateralTriangles(1000000000), 518408346);
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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 almostEquilateralTriangles(limit) {
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return true;
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}
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almostEquilateralTriangles(50);
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```
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# --solutions--
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```js
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function almostEquilateralTriangles(limit) {
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// Based on https://blog.dreamshire.com/project-euler-94-solution/
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let perimetersSum = 0;
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let sidesAB = 1;
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let sideC = 1;
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let perimeter = 0;
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let perimeterOffset = 1;
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while (perimeter <= limit) {
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[sidesAB, sideC] = [4 * sidesAB - sideC + 2 * perimeterOffset, sidesAB];
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perimeterOffset = -perimeterOffset;
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perimetersSum += perimeter;
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perimeter = 3 * sidesAB - perimeterOffset;
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}
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return perimetersSum;
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}
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```
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