Concept 5 of 8
Figure Matrix: Complete the Group
Today's big idea
Find the rule that carries one entry to the next, then test it on a second row.
Adding and doubling look identical at the start, which is why one row is not enough.
How it works
👀 What's going on?
A grid of shapes or numbers is shown with one cell left empty. Everything you need to fill it is already on the page, provided you work out what the rest of the grid is doing.
💡 Here's the trick
Look at the grid above. Read along a row or down a column and ask what turns one entry into the next. Once a rule fits every filled cell, the same rule fills the empty one. A rule that works for only part of the grid is the wrong rule.
🪄 How to do it
- 1.Read one full row or column of the grid above.
- 2.Work out the rule that carries each entry to the next.
- 3.Check the rule on a second row, then apply it to the gap.
✍️ Try it
A column reads 5, 10, 15 and then a gap. Then: a row reads 3, 6, 12 and then a gap.
The first column adds 5 each time, so the gap is 20. The second row doubles each time, so the gap is 24. Adding and doubling look alike at the start, which is why the rule must be tested twice.
⚠️ Watch out
You might be thinking the first rule that fits is the right one. Take 2, 4 and then 8, which could be doubling or could be adding 2 and then 4. Test your rule on another row before you trust it with the answer.
🌟 Why this matters
Filling a gap from a pattern is what you do reading a timetable or a price list with a smudge on it. The information is nearly always already there.
Exam tip: Check the columns as well as the rows, because some grids hide the rule in the direction you did not read.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“🔴 🔵 🟢 ? Slot 4 repeats slot 1. What colour?”
- 1
Read the rule
“Slot 4 = slot 1”.
- 2
Look at slot 1
Slot 1 = 🔴.
- 3
Apply
Slot 4 must be the same colour.
- 4
Answer ✓
Slot 4 = 🔴
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Find the repeating unit, then tap the tile that comes next.
PATTERN · ROUND 1 OF 3
Which tile comes next?
Quick check
✅ VERIFICATION
A rule for a grid can be trusted once it fits
⚡ Finish the activity above first to answer.
Keep going!
Up next: Cube Stack
Don't forget cubes hidden at the back.