Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 990 · 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 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 339 (c) 340 (d) 330
2. 2.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 50 (c) 49 (d) 58
3. 3.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 348 (c) 349 (d) 339
4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 16 (b) 14 (c) 4 (d) 15
5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 4 (b) 5 (c) 2 (d) 3
6. 6.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
7. 7.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 180 (c) 172 (d) 171
8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 3 (b) 15 (c) 14 (d) 13
9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 1 (d) 3
10. 10.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 18 (b) 17 (c) 16 (d) 6
12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 4 (b) 5 (c) 2 (d) 3
13. 13.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 5 (d) 14
14. 14.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 537 (c) 547 (d) 546
15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 17 (b) 16 (c) 5 (d) 15
16. 16.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 4 (b) 6 (c) 5 (d) 3
18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 16 (b) 15 (c) 5 (d) 17
19. 19.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 12 (c) 36 (d) 39
20. 20.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 480 (c) 392 (d) 481
21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 4 (d) 1
22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 15 (d) 14
23. 23.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) 69 (b) 72 (c) 207 (d) 23
24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 17 (d) 18
25. 25.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 114 (c) 124 (d) 123
26. 26.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 11 (c) 99 (d) 33
27. 27.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 75 (c) 24 (d) 72
28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 19 (b) 18 (c) 8 (d) 20
29. 29.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 223 (c) 222 (d) 213
30. 30.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 63 (b) 180 (c) 20 (d) 60
31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 20 (d) 9
32. 32.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 337 (c) 336 (d) 296
33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 16 (b) 15 (c) 17 (d) 5
34. 34.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
35. 35.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 135 (b) 144 (c) 126 (d) 136
36. 36.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 142 (c) 134 (d) 124
37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 18 (b) 17 (c) 19 (d) 8
38. 38.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) 21 (b) 54 (c) 6 (d) 18
39. 39.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 24 (c) 72 (d) 27
40. 40.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 362 (c) 435 (d) 426

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