Dominosa Techniques: Counting Pairs and Forcing Dominoes

Updated October 2026

Dominosa gives you a grid of digits and asks you to cut it into dominoes so that every pair from a full double-five set appears exactly once. There is nothing to guess: each board has a single answer, and every step towards it can be found by reasoning. This guide explains the shape of the puzzle, the facts you can count on before you start, and a set of deductions that solve boards quickly and without backtracking.

The puzzle in numbers

The board is 7 rows by 6 columns, 42 squares in all, each holding a digit from 0 to 5. A double-five set has 21 dominoes: the six doubles from 0-0 to 5-5 and the fifteen mixed pairs such as 0-3 or 2-5. Twenty-one dominoes of two squares each cover the 42 squares exactly, so every square belongs to one domino and every pair is used once.

Two less obvious facts follow. Every digit appears exactly seven times on the board, because each digit sits on five mixed dominoes and twice on its own double. And there are 71 places where a domino could lie: 35 side-by-side pairs of squares and 36 pairs one above the other. With 21 dominoes to choose from 71 spots, most of the work is ruling out spots.

The game checks every board with a solver before showing it and only accepts boards with exactly one solution. So if a deduction seems to leave two possibilities, a stronger deduction is available somewhere else on the board.

Placing and removing dominoes

Press on a square, slide to a square that touches it horizontally or vertically, and lift your finger: a domino appears across the two. Diagonal or distant releases are ignored. Pressing and lifting on the same square removes the domino covering it. If you lay a domino across squares that already belong to other dominoes, those dominoes are removed automatically, so you can correct a mistake in one stroke instead of clearing first.

Whenever the same pair appears on two dominoes, both are outlined in red. The board is complete when all 42 squares are covered and no pair is repeated; there is no separate check button. The clock starts when you press Start on the Ready card and stops on completion. Your time is rounded to whole seconds, and the lowest time is your best.

First pass: pairs that can only go in one place

Start by counting where each pair can appear. Doubles are the best place to begin, because a double needs two equal digits next to each other, which is relatively rare. In our simulation of 500 boards made by the game's own generator, doubles had about 2 possible spots on average, while mixed pairs had about 4. In the same simulation 95 percent of boards had at least one pair that appeared in exactly one place, and of the roughly 2.4 such pairs per board, about 1.9 were doubles.

So the opening is mechanical: scan the board for each double, 0-0 through 5-5. If a double shows up in only one place, lay it down at once. Then look for mixed pairs that appear only once, which takes longer because there are fifteen of them. A systematic order, such as all pairs containing 0, then all containing 1, prevents you from missing one.

Second pass: squares with one option left

Each placed domino does two things. It uses up its two squares, so neighbouring squares lose a possible partner. And it removes that pair everywhere else, so every other spot showing the same pair is now dead. After each placement, look at the squares around it and at the other places where its pair appeared.

The key question for each square is how many live partners it has left. A partner is live if it is next to the square, not yet covered, and the pair they would form has not been used. A square with exactly one live partner is forced. Corners start with only two neighbours and edge squares with three, so they reach this state first. The forced chain often runs along an edge: one placement fixes a corner, which fixes the next edge square, and so on.

Third pass: pairs with all their spots overlapping

When the first two passes stall, return to the pair counts with the dead spots removed. A pair that is now possible in only one live spot is forced, even if it had several spots at the start. Another strong pattern is a pair whose remaining spots all share one square. For example, if 3-4 can only lie across square A and the square to its right, or across square A and the square below it, then square A is certainly part of 3-4. That means A cannot pair with anything else, and its other neighbours lose A as a partner, which may force them.

The reverse also works. If a square's live partners would all form the same pair, then that pair belongs to that square, and every other spot of the pair elsewhere on the board is dead.

Using the red outline well

The red outline only tells you that a pair has been used twice; it does not tell you which copy is right. If you ever see red, do not guess. Remove the domino you placed most recently and recheck the reasoning behind it, because the earlier one was probably forced. Solving by deduction alone means you should never see red, so treat it as a sign that a step was skipped.

For speed, the biggest gain is not touching the screen until a domino is certain. Removing and replacing dominoes costs time twice: once for the strokes, and again for redoing the reasoning that depended on them.

A routine for every board

1. Scan all six doubles and place any that occur only once.
2. Scan the fifteen mixed pairs in a fixed order and place any unique ones.
3. After every placement, check the neighbours of its two squares and the other spots of its pair.
4. Work along edges and corners, where squares run out of partners first.
5. When stuck, recount the live spots of each unused pair and look for spots sharing a square.
6. Finish the last few dominoes quickly; by then each remaining square usually has one partner.

Your best time stays on your device, and completed times can be saved to the Hall of Fame. Once counting doubles and tracking dead spots becomes routine, a board that took several minutes at first becomes a steady chain of forced moves.