Number puzzles and digit counting — Maths Olympiad practice

How to solve it

Count place by place — “split the count into ones, tens and hundreds”

1. Count a digit place by place: first in the ones place, then in the tens place (a number like 33 counts twice).
2. Page numbers: pages 1–9 use 1 digit each, 10–99 use 2, 100–999 use 3.
3. A 3 × 3 magic square made of nine numbers: each row adds up to (sum of all nine) ÷ 3.

Use it for: Digit counting, page numbering, magic square and digit-sum puzzles in Class 5–8 Olympiad papers.

Worked example: A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? → 252

✏️ Practice

Work it out on paper, then tap the answer you think is right. Stuck? Press “Show me how” to see every step.

🏁 Topic 25 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 ✨ Magic Square Maker badge when you pass — and a certificate when you finish all 13 topics of Part 4 · Class 5–10 problem solving. You can still take the test without signing in.

🖨️ Number Puzzles Worksheet for Maths Olympiad

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