Concept 2 of 6
Repeating Patterns: Find the Core, Reach Any Slot
Today's big idea
One core, repeated: carry it on for the next item, or divide the slot to reach any slot.
Core = circle, triangle, square. Slot 8 lands on the 2nd shape, the triangle.
How it works
👀 What's going on?
A repeating pattern is built from one small chunk shown over and over. Find that chunk and the whole strip is yours: you can say what comes next, or jump straight to a far slot without drawing it.
💡 Here's the trick
Look at the pattern above: circle, triangle, square, then circle, triangle, square again. That repeating chunk is called the core, and here it is 3 shapes long. The next shape is simply whatever comes next inside the core, wrapping back to the start at the end. To reach a far slot like 20 you do not draw it out. Divide the slot number by the core length: 20 ÷ 3 = 6, with 2 left over. That leftover of 2 counts into the core, landing on the 2nd shape, the triangle. A leftover of 0 lands on the last shape of the core.
🪄 How to do it
- 1.Find the core in the picture above, the shortest chunk that repeats, and count its shapes.
- 2.For the very next shape, just carry the core on; for a far slot, divide the slot number by the core length.
- 3.The leftover names the shape: 1 is the 1st, 2 the 2nd, and 0 the last.
✍️ Try it
A pattern repeats red, blue, green, yellow over and over. What sits in slot 30? And what sits in slot 40?
The core is 4 long. Slot 30: 30 ÷ 4 is 7 with 2 left over, so it is the 2nd colour, blue. Slot 40: 40 ÷ 4 is 10 with 0 left over, and 0 means the last colour, yellow.
⚠️ Watch out
A leftover of 0 does not mean something went wrong. It means the slot lands exactly at the end of a core, so it is the last item. Slot 40 with a 4-long core is just the tenth repeat finishing.
🌟 Why this matters
Days of the week work exactly like this, which is how you can name the day 30 days from now without counting them off. Beads on a bracelet and tiles along a wall behave the same way.
Exam tip: Divide and take the leftover rather than drawing the pattern out, because papers ask for slot 50 precisely to stop you drawing.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
“Pattern: ⭐ 🌙 ☀️ ⭐ 🌙 ☀️ ⭐ ? Slot 8?”
- 1
Find the core
Shortest repeating unit = ⭐ 🌙 ☀️. Length = 3.
- 2
Which slot in the core?
Position 8 → (8 − 1) mod 3 = 1 → second slot.
- 3
Look up that slot
Second slot of the core = 🌙.
- 4
Answer ✓
Slot 8 = 🌙
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Find the CORE — the shortest group that repeats — then count to the gap.
PATTERN · ROUND 1 OF 3
Core length: 2 · Gap at position 6
Tap the shape that fills position 6:
Quick check
✅ VERIFICATION
A pattern repeats A, B, C, D, E over and over. Which letter is in slot 17?
⚡ Finish the activity above first to answer.
Keep going!
Up next: Alphabet Series
+1, +2, or backwards: same step every time.