32fac23a2d
* fix: clean-up Project Euler 161-180 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
54 lines
1.6 KiB
Markdown
54 lines
1.6 KiB
Markdown
---
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id: 5900f40f1000cf542c50ff22
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title: 'Problem 163: Cross-hatched triangles'
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challengeType: 5
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forumTopicId: 301797
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dashedName: problem-163-cross-hatched-triangles
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---
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# --description--
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Consider an equilateral triangle in which straight lines are drawn from each vertex to the middle of the opposite side, such as in the size 1 triangle in the sketch below.
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<img class="img-responsive center-block" alt="triangles with size 1 and size 2" src="https://cdn.freecodecamp.org/curriculum/project-euler/cross-hatched-triangles.gif" style="background-color: white; padding: 10px;">
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Sixteen triangles of either different shape or size or orientation or location can now be observed in that triangle. Using size 1 triangles as building blocks, larger triangles can be formed, such as the size 2 triangle in the above sketch. One-hundred and four triangles of either different shape or size or orientation or location can now be observed in that size 2 triangle.
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It can be observed that the size 2 triangle contains 4 size 1 triangle building blocks. A size 3 triangle would contain 9 size 1 triangle building blocks and a size $n$ triangle would thus contain $n^2$ size 1 triangle building blocks.
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If we denote $T(n)$ as the number of triangles present in a triangle of size $n$, then
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$$\begin{align}
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& T(1) = 16 \\\\
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& T(2) = 104
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\end{align}$$
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Find $T(36)$.
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# --hints--
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`crossHatchedTriangles()` should return `343047`.
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```js
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assert.strictEqual(crossHatchedTriangles(), 343047);
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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 crossHatchedTriangles() {
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return true;
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}
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crossHatchedTriangles();
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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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