yaworsw/euler-manager

---
:id: 275
:name: Balanced Sculptures
:url: https://projecteuler.net/problem=275
:content: "Let us define a _balanced sculpture_ of order <var>n</var> as follows:\n\n-
  A <dfn title=\"An arrangement of identical squares connected through shared edges;
  holes are allowed.\">polyomino</dfn> made up of <var>n</var>+1 tiles known as the
  _blocks_ (<var>n</var> tiles)  \n and the _plinth_ (remaining tile);\n- the plinth
  has its centre at position (<var>x</var> = 0, <var>y</var> = 0);\n- the blocks have
  <var>y</var>-coordinates greater than zero (so the plinth is the unique lowest tile);\n-
  the centre of mass of all the blocks, combined, has <var>x</var>-coordinate equal
  to zero.\n\nWhen counting the sculptures, any arrangements which are simply reflections
  about the <var>y</var>-axis, are <u>not</u> counted as distinct. For example, the
  18 balanced sculptures of order 6 are shown below; note that each pair of mirror
  images (about the <var>y</var>-axis) is counted as one sculpture:\n\n ![p275_sculptures2.gif]({{
  images_dir }}/p275_sculptures2.gif)\n\nThere are 964 balanced sculptures of order
  10 and 360505 of order 15.  \nHow many balanced sculptures are there of order 18?\n\n"