Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 656 · 40 questions

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

1. 1.The numbers 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 51 (b) 16 (c) 48 (d) 144
2. 2.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 42 (c) 126 (d) 14
3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 19 (b) 21 (c) 9 (d) 20
4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 6 (b) 7 (c) 5 (d) 8
5. 5.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 379 (b) 378 (c) 369 (d) 324
6. 6.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 45 (c) 15 (d) 5
7. 7.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 60 (c) 78 (d) 70
8. 8.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 619 (c) 484 (d) 609
9. 9.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 21 (b) 63 (c) 24 (d) 7
10. 10.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 72 (c) 82 (d) 81
11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 3 (b) 5 (c) 2 (d) 4
12. 12.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 117 (c) 13 (d) 42
13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 5 (b) 7 (c) 6 (d) 8
14. 14.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 597 (c) 470 (d) 588
15. 15.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 33 (c) 90 (d) 30
16. 16.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 15 (b) 6 (c) 14 (d) 16
18. 18.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
19. 19.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 66 (c) 63 (d) 21
20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 19 (d) 18
21. 21.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 18 (b) 54 (c) 21 (d) 6
22. 22.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
23. 23.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 45 (c) 135 (d) 48
24. 24.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 333 (c) 300 (d) 343
25. 25.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 384 (c) 469 (d) 468
26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 14 (d) 5
27. 27.A book has 214 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 428 (b) 535 (c) 534 (d) 525
28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 16 (b) 4 (c) 15 (d) 14
29. 29.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 114 (c) 113 (d) 122
30. 30.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
31. 31.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
32. 32.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 21 (d) 19
34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 8 (b) 12 (c) 13 (d) 10
35. 35.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 54 (b) 17 (c) 153 (d) 51
36. 36.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 9 (c) 81 (d) 30
37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 53? (a) 6 (b) 3 (c) 4 (d) 5
38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 7 (b) 6 (c) 8 (d) 9
39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 8 (b) 6 (c) 7 (d) 5
40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 68? (a) 6 (b) 4 (c) 7 (d) 5

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad