Repeating patterns — Logical reasoning for kids

How to think it through

Use the remainder — “the remainder after dividing by the pattern length tells you the place in the pattern”

1. Find the repeating part and count how long it is (for example 3 items).
2. Divide the position you want by that length and find the remainder.
3. Remainder 1 → first item, remainder 2 → second item … remainder 0 → the last item of the pattern.

Use it for: Pattern questions in Olympiads, bead and rangoli patterns, and days of the week.

Worked example: This pattern keeps repeating: red, blue, green, red, blue, green, … Which comes 20th? Blue

✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

🏁 Lesson 5 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the 🔁 Pattern Prophet badge when you pass — and a certificate when you finish all 10 lessons of Part 1 · Patterns. You can still take the test without signing in.

🖨️ Repeating Patterns Worksheet

• Worksheet set 1 (PDF)
• Worksheet set 2 (PDF)
• Worksheet set 3 (PDF)