freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-189-tri-colouring-a-triangular-grid.english.md

id	challengeType	title	forumTopicId
5900f4291000cf542c50ff3c	5	Problem 189: Tri-colouring a triangular grid	301825

Description

Consider the following configuration of 64 triangles:

We wish to colour the interior of each triangle with one of three colours: red, green or blue, so that no two neighbouring triangles have the same colour. Such a colouring shall be called valid. Here, two triangles are said to be neighbouring if they share an edge. Note: if they only share a vertex, then they are not neighbours.

For example, here is a valid colouring of the above grid:

A colouring C' which is obtained from a colouring C by rotation or reflection is considered distinct from C unless the two are identical.

How many distinct valid colourings are there for the above configuration?

Instructions

Tests

tests:
  - text: <code>euler189()</code> should return 10834893628237824.
    testString: assert.strictEqual(euler189(), 10834893628237824);

Challenge Seed

function euler189() {
  // Good luck!
  return true;
}

euler189();

Solution

// solution required