Dominosa
Place every domino exactly once
Dominosa is a domino-placement logic puzzle where you tile a rectangular grid with a complete set of dominoes. The grid shows numbers, and you must pair adjacent cells into dominoes so that every possible number combination appears exactly once. For a set using numbers 0 through N, every pair (0-0, 0-1, 0-2, ..., N-N) must be placed. The constraint that each domino appears exactly once transforms a simple matching problem into a rich deductive challenge.
How to Play Dominosa
Number Grid
The grid is filled with numbers. Each cell contains a single digit from 0 to N.
Pair Adjacent Cells
Draw borders to pair every two orthogonally adjacent cells into a domino. Each domino covers exactly two cells.
Complete Set
Every possible number pair must appear exactly once: (0,0), (0,1), (0,2), ..., up to (N,N).
No Duplicates
The domino (2,5) and the domino (5,2) are the same piece. It can only appear once in the entire grid.
Full Coverage
Every cell must be part of exactly one domino. No cells are left unpaired.
Unique Solution
The combination of the complete-set constraint with the specific number layout guarantees exactly one valid tiling.
Strategy & Solving Tips
Dominosa solving is about uniqueness — finding number pairs that can only be matched in one place on the grid.
- Start by finding number pairs that appear adjacent only once on the grid — these dominoes are immediately determined
- After placing a domino, cross it off the list of available dominoes. This may make other pairs unique
- When a pair appears adjacent in multiple locations, skip it and work on uniquely-determined pairs first
- Placing a domino removes those cells from other potential pairings, often creating new forced placements
- Track which dominoes remain to be placed — as the list shrinks, more placements become forced
- Pay attention to number frequency: a digit that appears many times creates many domino options, while rare digits are more constraining
Dominosa FAQ
How many dominoes are in a complete set?
For numbers 0 through N, the set contains (N+1)(N+2)/2 dominoes. For 0-6, that's 28 dominoes. For 0-9, it's 55. The grid dimensions are designed to fit exactly one complete set.
Is (3,5) the same as (5,3)?
Yes. Dominoes are unordered pairs. Whether the 3 is on the left and the 5 on the right (or vice versa) doesn't matter — it's the same domino and can only appear once.
What if multiple pairings seem possible?
The puzzle has exactly one solution, so seemingly ambiguous situations are resolved by constraints elsewhere on the grid. Place the dominoes you're sure about first, and the remaining options will narrow.
Can a domino be placed diagonally?
No. Dominoes always cover two orthogonally adjacent cells — horizontally or vertically, never diagonally.
Ready to Play Dominosa?
Match every number pair in Dominosa — the domino puzzle where the complete set constraint turns simple pairing into deep logical deduction.