The number of distinct valid Tango boards grows rapidly with grid size. No closed-form formula is known. These counts were found by exhaustive search with pruning optimizations.
| Grid size | Valid boards |
|---|---|
2 × 2 |
2 |
4 × 4 |
90 |
6 × 6 |
11,222 |
8 × 8 |
12,413,918 |
10 × 10 |
117,925,227,108 |
A valid board is any complete assignment of suns and moons that satisfies the row and column balance and adjacency rules, ignoring = and × constraints between cells. The number of solvable Tango puzzles (given cells plus edge markers that yield a unique solution) is a separate, much larger question.