freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-275-balanced-sculptures.english.md

id	challengeType	title
5900f4801000cf542c50ff92	5	Problem 275: Balanced Sculptures

Description

Let us define a balanced sculpture of order n as follows: A polyomino made up of n+1 tiles known as the blocks (n tiles) and the plinth (remaining tile); the plinth has its centre at position (x = 0, y = 0); the blocks have y-coordinates greater than zero (so the plinth is the unique lowest tile); the centre of mass of all the blocks, combined, has x-coordinate equal to zero. When counting the sculptures, any arrangements which are simply reflections about the y-axis, are not counted as distinct. For example, the 18 balanced sculptures of order 6 are shown below; note that each pair of mirror images (about the y-axis) is counted as one sculpture:

There are 964 balanced sculptures of order 10 and 360505 of order 15.How many balanced sculptures are there of order 18?

Instructions

Tests

tests:
  - text: <code>euler275()</code> should return 15030564.
    testString: assert.strictEqual(euler275(), 15030564, '<code>euler275()</code> should return 15030564.');

Challenge Seed

function euler275() {
  // Good luck!
  return true;
}

euler275();

Solution

// solution required