41 lines
1.3 KiB
Markdown
41 lines
1.3 KiB
Markdown
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---
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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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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. 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 n2 size 1 triangle building blocks. If we denote T(n) as the number of triangles present in a triangle of size n, then T(1) = 16 T(2) = 104 Find T(36).
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# --hints--
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`euler163()` should return 343047.
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```js
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assert.strictEqual(euler163(), 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 euler163() {
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return true;
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}
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euler163();
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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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