Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 724 · 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.How many times is the digit 6 written when you write all the numbers from 1 to 56? (a) 6 (b) 4 (c) 7 (d) 5
2. 2.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
3. 3.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 8 (b) 11 (c) 14 (d) 13
5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 4 (d) 2
6. 6.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) 17 (b) 153 (c) 51 (d) 54
7. 7.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 523 (c) 513 (d) 522
8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 17 (d) 18
9. 9.The numbers 18 to 26 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) 198 (c) 22 (d) 66
10. 10.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 555 (c) 564 (d) 565
11. 11.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
12. 12.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
13. 13.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 258 (c) 279 (d) 270
14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 19 (b) 17 (c) 18 (d) 7
15. 15.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
16. 16.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
17. 17.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 174 (c) 164 (d) 173
18. 18.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 624 (b) 634 (c) 633 (d) 494
19. 19.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
20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 6 (b) 17 (c) 15 (d) 16
21. 21.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 110 (c) 102 (d) 101
22. 22.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 131 (b) 132 (c) 122 (d) 140
23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 15 (b) 16 (c) 17 (d) 5
24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 15 (b) 17 (c) 6 (d) 16
25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 2 (d) 3
26. 26.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
27. 27.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) 6 (b) 21 (c) 54 (d) 18
28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 17 (d) 7
29. 29.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) 33 (d) 99
30. 30.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 121 (b) 122 (c) 130 (d) 112
31. 31.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 398 (c) 489 (d) 490
32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 3 (b) 13 (c) 15 (d) 14
33. 33.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 194 (c) 186 (d) 176
34. 34.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 109 (c) 110 (d) 100
35. 35.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) 171 (b) 60 (c) 57 (d) 19
36. 36.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 415 (c) 348 (d) 414
37. 37.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 318 (c) 360 (d) 370
38. 38.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
39. 39.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 72 (c) 71 (d) 80
40. 40.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 192 (c) 201 (d) 202

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