How to solve distribution puzzles

Last updated November 1, 2026

In a distribution puzzle, each row and each column contains every value of a property exactly once, like a small Sudoku of shapes: one circle, one square and one hexagon per row, or one solid, one hollow and one dotted fill. To solve it, list what the last row already has for each property and pick the option that adds the one missing value of every property at once.

What a distribution puzzle looks like

Distribution puzzles look random at first because nothing changes in a steady direction. The order inside each row is shuffled, but the set of values is the same in every row and every column.

In our set the distributed property can be the shape, the fill, the size or the size of a group, and the harder puzzles distribute two or three properties at once, or run a distribution beside a count that drops along the row.

Worked example: Puzzle #7, Fills and Shapes

Pick an option first, then open the solution.

Which option completes the pattern?

How to solve it (answer: E)

The rule

Each row and each column has one hollow, solid, and dotted shape and one triangle, pentagon, and hexagon.

Step by step

Look at the top row: a solid triangle, then a dotted hexagon, then a hollow pentagon.
The middle row uses the same values in a different order.
The bottom row has a dotted pentagon and a hollow triangle, so it is missing a solid hexagon.
Check both rules: only one option fits them both.

Tip: List what each row already has, then pick the one value the row is missing.

A method for distribution puzzles

Pick one property, such as shape, and list its values in the top row.
Check that the second row uses the same values in another order. If it does, the property is distributed.
Repeat for every other property: fill, size, count.
For the bottom row, write down the missing value of each distributed property.
Choose the only option that has all the missing values together. Check the column as well as the row.

Why the wrong options look right

Right shape, repeated fill

The most common wrong option completes the shapes and repeats a fill already in the row. It looks finished because the first property you checked was right.

Checking only the row

Each column follows the rule too. When two options both fit the row, the column decides.

A hidden third property

Size and group count are easy to miss. When an option seems right on shape and fill, check the size and the number of shapes too.

The variants in this set

One of each shape per row and column.
One of each fill per row and column.
One of each size per row and column.
Shapes and sizes distributed together, or shapes and group counts.
Shape, fill and group count distributed at once.

Practice: 9 distribution puzzles

The other pattern types

Distribution is one of four pattern types

The Cogniva test has five puzzles of each type, 20 in all, and gives you a free score band in about 7 minutes. The full report shows how you did on each type.

Take the 20-question test

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