How to solve number grid puzzles
Number grids: rows, columns, then corners
A number matrix hides its rule in the rows or the columns. Interrogate them in order and the missing cell computes itself.
Updated
In a 3×3 number grid, the rule is one of two kinds: the third number in each row is computed from the first two (+, −, ×, or ×-then-add), or each column climbs by a constant step. That's a short list — test it in order.
Row operations first
Check: does first ∘ second = third hold across the complete rows for one operation ∘? Test + first, then −, then ×, then × with an adjustment. Two rows confirming the same operation is proof; apply it to the incomplete row.
Then column steps
If no row operation fits, subtract down each column: constant steps mean the missing cell continues its column.
The strategy
- Read the grid row-wise aloud: 'four, three, twelve' — products and sums jump out when verbalized.
- Confirm any candidate rule on BOTH complete rows (or both complete columns) before using it.
- Compute the missing value, then match — never work backwards from the options.
- Large third numbers hint ×; smaller-than-both hint −; between the two hints column rules.
Common traps
- A rule that fits one row only — coincidences are common with small numbers.
- Mixing directions mid-grid (row logic on rows one and two, column logic to 'finish').
- The distractor equal to a nearby cell's value.
Speed · ~40s/item: Under 45 seconds once the testing order is habit: row operations, then column steps — in that order, always.
Try it yourself: 4 practice questions
Pick an answer, then reveal it. Nothing is recorded, there is no clock, and none of these questions is ever used in a test.
The numbers follow one rule across every row or down every column. What number replaces the question mark?
Reveal the answer
The answer is B — 22.
Show why — the worked reasoning
The numbers follow one rule across every row or down every column. What number replaces the question mark?
Reveal the answer
The answer is C — 12.
Show why — the worked reasoning
The numbers follow one rule across every row or down every column. What number replaces the question mark?
Reveal the answer
The answer is C — 20.
Show why — the worked reasoning
The numbers follow one rule across every row or down every column. What number replaces the question mark?
Reveal the answer
The answer is C — 12.
Show why — the worked reasoning
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Questions people ask
Will number grids questions be on the free test?
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