Matrix reasoning involves comparing relationships across rows, columns or positions, then judging the missing part. Finding a seemingly plausible rule is only the beginning; check whether it also explains the other known positions.
The following teaching material was created for this page. It is not a question from this site's bank or a sample from any formal assessment. Arrows indicate direction and numbers indicate how many identical arrows appear.
| Position | First cell | Second cell | Third cell |
|---|
| First row | 1 ↑ | 2 → | 3 ↓ |
| Second row | 2 ↑ | 3 → | 4 ↓ |
|
First consider quantity alone: moving right adds 1 in each row, and moving down adds 1 in each column, so the missing cell should contain 5. Next consider direction: every row follows ↑, →, ↓, while direction stays constant within a column, so the missing cell should contain 5 ↓.
One tempting mistake is to say “the shapes always rotate clockwise”. This explains the change from left to right but not from top to bottom: the first column always points ↑ and does not rotate. Revise the rule to “direction changes horizontally and stays constant vertically”, rather than ignoring counterexamples to preserve a guess.
This example also shows that the correct quantity is not a complete answer: 5 → satisfies the quantity condition but violates the third column's direction condition. Work through four steps: describe observations, propose a rule, check every known position, and confirm that the answer satisfies every condition. Limited material may not exclude every imaginable rule; the teaching example uses a simple rule that consistently explains the known information, rather than proving someone's intelligence level.