freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-163-cross-hatched-triangles.english.md

id, challengeType, title, forumTopicId

id	challengeType	title	forumTopicId
5900f40f1000cf542c50ff22	5	Problem 163: Cross-hatched triangles	301797

Description

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.

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).

Instructions

Tests

tests:
  - text: <code>euler163()</code> should return 343047.
    testString: assert.strictEqual(euler163(), 343047);

Challenge Seed

function euler163() {
  // Good luck!
  return true;
}

euler163();

Solution

// solution required