Problem 44735. Aztec Diamond domino tilings

  • Created by HH

Consider a Cartesian grid, with verteces at integer x and y values, where every four vertices around a vacant space define a unit square. An Aztec Diamond of order d is the shape formed by all unit squares whose centers satisfy the equation:

abs(x) + abs(y) <= d

Given the order of an Aztec Diamond, d (positive integer), return the number, n, of possible tilings using domino tiles, i.e. rectangles sized 1x2 and 2x1, such that:

  1. The entire shape is covered
  2. There are no overlapping tiles
  3. None of the tiles stick out of the shape


An Aztec Diamond of order 4 is shown at this URL.

Input: d = 4

Output: n = 1024

Solution Stats

73.91% Correct | 26.09% Incorrect
Last Solution submitted on Jun 06, 2022

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