freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-275-balanced-sculptures.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f4801000cf542c50ff92	Problem 275: Balanced Sculptures	5	301925	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?

--hints--

balancedSculptures() should return 15030564.

assert.strictEqual(balancedSculptures(), 15030564);

--seed--

--seed-contents--

function balancedSculptures() {

  return true;
}

balancedSculptures();

--solutions--

// solution required