Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 331 · 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.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 122 (c) 113 (d) 104
2. 2.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
3. 3.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 149 (c) 158 (d) 140
4. 4.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
5. 5.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 155 (c) 156 (d) 146
6. 6.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 60 (b) 19 (c) 57 (d) 171
7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 37? (a) 15 (b) 13 (c) 3 (d) 14
8. 8.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 57 (b) 162 (c) 18 (d) 54
9. 9.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 7 (d) 9
10. 10.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 452 (c) 570 (d) 571
11. 11.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 379 (c) 378 (d) 369
12. 12.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) 48 (c) 16 (d) 144
13. 13.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) 117 (b) 42 (c) 39 (d) 13
14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 2 (b) 5 (c) 4 (d) 3
15. 15.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 556 (c) 546 (d) 442
16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 67? (a) 7 (b) 6 (c) 4 (d) 5
17. 17.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
18. 18.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 107 (b) 108 (c) 116 (d) 98
19. 19.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 458 (c) 579 (d) 580
20. 20.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
21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 2 (b) 5 (c) 3 (d) 4
22. 22.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 457 (b) 447 (c) 376 (d) 456
23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 87? (a) 7 (b) 8 (c) 6 (d) 9
24. 24.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 630 (c) 631 (d) 492
25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 4 (d) 16
26. 26.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) 45 (b) 135 (c) 48 (d) 15
27. 27.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 400 (c) 338 (d) 399
28. 28.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 174 (c) 183 (d) 184
29. 29.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 91 (c) 82 (d) 100
30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 1 (b) 2 (c) 4 (d) 3
31. 31.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) 15 (b) 5 (c) 18 (d) 45
32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 16 (b) 4 (c) 14 (d) 15
33. 33.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 540 (c) 531 (d) 541
34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 7 (b) 17 (c) 18 (d) 19
35. 35.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
36. 36.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
37. 37.The numbers 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 72 (c) 23 (d) 69
38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 9 (b) 6 (c) 8 (d) 7
39. 39.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
40. 40.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 520 (b) 510 (c) 519 (d) 418

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