The Aztec Diamond
The Aztec diamond of order 4 is the region of the square grid made of 8 rows of unit squares whose lengths are 2, 4, 6, 8, 8, 6, 4, 2, with every row centred on the same vertical axis (equivalently, the union of all unit grid squares whose centres satisfy |x| + |y| ≤ 4). It contains 40 squares. In how many ways can this region be tiled exactly by 20 dominoes (1 × 2 rectangles placed horizontally or vertically)? Give an integer.
Related problems & prerequisites
Worth solving first
- Dominoes on a 3 × 10 Board 6.0/10
- Strides of Any Length 5.4/10
- No Three Alike 5.0/10
Source: Aztec diamonds and their tiling count are due to N. Elkies, G. Kuperberg, M. Larsen and J. Propp (1992). Statement written for AxiomIQ.