How to solve combination puzzles

Last updated November 1, 2026

In a combination puzzle, the third cell of each row is built from the first two: it keeps every mark from both, only the marks they share, only the marks that appear in one of them, or the first cell's marks minus the second's. To solve it, compare the first two cells mark by mark, test each of those four rules on the third cell, and keep the one that works in every row.

What a combination puzzle looks like

Combination puzzles look like overlays: lines, dots or small shapes laid over each other. Unlike a progression, nothing moves. The question is which marks survive when two cells meet.

Our set uses the four rules that cover most overlay puzzles: keep all marks (union), keep the shared ones (intersection), keep the ones in only one cell (exclusive), and subtract the second cell from the first (difference). In the hardest ones, a second rule distributes the shapes across rows at the same time.

Worked example: Puzzle #13, Shared Marks

Pick an option first, then open the solution.

Which option completes the pattern?

How to solve it (answer: B)

The rule

The third panel in each row keeps only the marks both panels share.

Step by step

Look at the top row: the left side and the bottom left dot, then four marks, then the bottom left dot.
The middle row follows the same rule.
Apply the same rule to the bottom row: the answer shows the bottom right dot.

Tip: Compare the first two panels mark by mark, then test each rule on the third panel.

A method for combination puzzles

In the top row, list the marks of the first cell and of the second.
Sort them into three groups: in both cells, only in the first, only in the second.
Look at the third cell and see which groups it kept.
Name the rule: all three groups is union, the shared group is intersection, the two single groups is exclusive, the first-only group is difference.
Test the rule on the second row, then build the missing cell from the bottom row's first two cells.

Why the wrong options look right

Union by habit

Keeping every mark is the rule people reach for first, so an option with all the marks of both cells is offered in almost every combination puzzle. Test it, don't assume it.

One extra mark

Wrong options often add a single mark that appears in neither cell. Count the marks of your answer against the two cells it comes from.

Shared versus exclusive

Intersection and exclusive are opposites, and each wrong option for one is often the answer to the other. Decide which group the third cell kept before you look at the options.

The variants in this set

Keep every mark from both cells.
Keep only the marks both cells share.
Keep the marks that appear in only one cell.
Keep the first cell's marks that the second cell lacks.
An exclusive rule on marks with one of each shape per row and column.

Practice: 7 combination puzzles

The other pattern types

Combination 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

Free to take. Report $29.90 once, tax included. 14-day refund.