Concept 4 of 9
Figure Matrix: 3x3 Grid Patterns
Today's big idea
Test the rows for a rule, then check the columns agree before filling the gap.
A rule that fits the rows can fail the columns, which means it is the wrong rule.
How it works
👀 What's going on?
Eight cells are filled and one sits empty, and the rule could be running across the rows, down the columns, or both at once.
💡 Here's the trick
Look at the grid above. Test the rows first, then test the columns. A rule that holds in both directions is almost certainly the one intended.
🪄 How to do it
- 1.Read each row of the grid above and look for a rule.
- 2.Read each column and check the same rule holds.
- 3.Apply whichever rule survives to the empty cell.
✍️ Try it
Every row sums to 24, and row 3 reads 9, then a gap, then 7. What fills the gap? Then: a column doubles going down and reads 3, 6, and a gap.
24 minus 9 minus 7 leaves 8. Doubling 6 gives 12.
⚠️ Watch out
You might be thinking one direction is enough to settle it. A rule that fits the rows can fail the columns, and when the two disagree you have almost certainly read the wrong rule.
🌟 Why this matters
Spotting the pattern in a table of numbers is the same skill, whether it is a timetable or a price list.
Exam tip: Check your answer against the other direction before you commit to it.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Each row of a 3×3 grid sums to 30. Row 3: 11, ?, 13. Find the missing number.”
- 1
Use the row rule
11 + ? + 13 = 30
- 2
Solve for ?
? = 30 − 24 = 6.
- 3
Answer ✓
6
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Look at the two full rows to spot the rule, then use it to fill the missing cell (?).
MATRIX · ROUND 1 OF 3
Quick check
✅ VERIFICATION
Every row of a grid has a product of 36. Row 2 reads 2, 9 and one more number. What is it?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Cubes & Dice
Opposite faces always add to 7. 1↔6 · 2↔5 · 3↔4.