How to solve a Quiltoku puzzle

You do not need to know Sudoku, and you do not need to be good with numbers. If you can look at a row of coloured squares and see which colour is missing, you already know the main trick. This guide walks through it step by step on a tiny board, then shows how the same idea grows to the big ones.

The one rule

Every row, every column and every box has to contain each mark exactly once. A "mark" is whatever the board is using: colours, shapes or patterns. A 4×4 board has four marks, a 6×6 board has six, a 9×9 board has nine. The boxes are the blocks drawn with a thicker outline: 2×2 on a 4×4 board, 2×3 on a 6×6, 3×3 on a 9×9.

A 4×4 board. The thick lines mark four boxes of 2×2. One square is empty and outlined in orange.

Technique 1: what is missing from the row?

This is the one to learn first, and on easy puzzles it solves nearly everything. Pick any row, count the marks it already has, and ask which one is not there yet.

The top row (shaded) already has red, green and yellow. Only blue is missing, so the empty square has to be blue.

The same works for columns and boxes. When a row, a column or a box is nearly full, the missing mark is handed to you. Scan the board for the fullest lines first. They are the cheapest wins, and each one you fill in makes the next one easier.

Technique 2: what is missing from the box?

Boxes are the part newcomers forget to look at, and they are often where the answer hides.

The top-left box (shaded) has red, green and blue. The empty square is inside it, so it has to be yellow.

Get in the habit of checking all three lines through a square: its row, its column and its box. A square sits in exactly one of each.

Technique 3: combine two lines

Sometimes a single line leaves two possible marks. Then you cross-check with another line that passes through the same square.

The row (shaded) leaves two squares open, so the marks left over are red and yellow. The column (also shaded) already has a red lower down, so the outlined square cannot be red. It is yellow.

Notice what happened: neither line was enough on its own, and together they were. Most medium puzzles are made of this one move repeated. If you are stuck, pick one empty square and write down in your head the marks its row rules out, then the marks its column rules out, then its box. What is left is its answer, or its short list of answers.

Technique 4: where can this mark go?

So far you asked "what goes in this square?" The other half of the skill is to turn it around and ask "where can this mark go in this row?" Pick a mark, say orange, and look at one box. Cross out every square in that box where orange is already ruled out by a row or a column. If only one square survives, that is where the orange goes, even if you do not yet know what any of the other squares in the box are.

This is the move that opens up the 9×9 boards. With nine marks, asking "what is missing from this line?" often gives you three or four candidates. Asking "where can orange go in this box?" usually gives you one.

When you are stuck

Start with the fullest line. A row with only one empty square is a gift. A row with two empty squares is nearly as good.
Work one mark at a time. Choose the mark that appears most often on the board and find where it still fits. Marks that are already common are the easiest to place.
Look at the board from a different side. Your eye gets used to rows. Switch to columns, then to boxes.
Use the flash. The 🔦 button points at a square you can solve right now without giving the answer away. It costs nothing, so it is the kindest way to get going again.
Use the bookmark. If you have to guess, tap ☆ first. If the guess turns out wrong, one tap returns you to where you were.
Walk away. Puzzles that stall at one o'clock are often solved in thirty seconds at two.

The same ideas on bigger boards

Nothing new is added on 6×6 and 9×9 boards. The rows and columns are longer, the boxes are bigger, and there are more marks to keep track of, but the four techniques above are the whole toolbox. What changes is how long it takes to look. That is why the daily puzzle gets bigger toward the weekend.

A 9×9 board with nine colours. The shaded box is the top-left 3×3. Same rule, same four techniques.

Every puzzle has exactly one answer

Each Quiltoku puzzle is built so that there is one and only one way to finish it. That means you never have to guess. If you reach a point where nothing seems to work, there is always a next square that can be proved from what is on the board. It is just hiding. The puzzles are checked by the game before they are ever shown to you.

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