Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 279 · 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 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) 6 (d) 21
2. 2.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 126 (c) 118 (d) 117
3. 3.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
4. 4.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) 180 (b) 20 (c) 63 (d) 60
5. 5.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 115 (b) 116 (c) 124 (d) 106
6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 6 (d) 18
7. 7.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 330 (c) 292 (d) 331
8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 20 (d) 9
9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 6 (b) 17 (c) 18 (d) 16
10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 1 (b) 2 (c) 4 (d) 3
11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 15 (b) 14 (c) 5 (d) 16
12. 12.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) 19 (b) 57 (c) 60 (d) 171
13. 13.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 426 (c) 532 (d) 522
14. 14.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 570 (c) 580 (d) 579
15. 15.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 226 (c) 225 (d) 222
16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 13 (b) 9 (c) 11 (d) 14
17. 17.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 3 (d) 5
18. 18.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) 11 (b) 33 (c) 36 (d) 99
19. 19.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 10 (d) 6
20. 20.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 62 (c) 80 (d) 72
21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 20 (d) 9
22. 22.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) 23 (c) 69 (d) 72
23. 23.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
24. 24.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 288 (c) 298 (d) 270
25. 25.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) 7 (b) 63 (c) 24 (d) 21
26. 26.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 95 (b) 96 (c) 86 (d) 104
27. 27.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) 198 (b) 69 (c) 22 (d) 66
28. 28.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 11 (d) 8
29. 29.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 218 (c) 220 (d) 219
30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 6 (b) 16 (c) 15 (d) 17
31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 8 (b) 7 (c) 6 (d) 5
32. 32.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 628 (b) 490 (c) 618 (d) 627
33. 33.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
34. 34.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) 39 (b) 36 (c) 12 (d) 108
35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 16 (b) 4 (c) 14 (d) 15
36. 36.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
37. 37.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
38. 38.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 352 (c) 342 (d) 351
39. 39.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 51 (c) 60 (d) 52
40. 40.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) 45 (b) 5 (c) 18 (d) 15

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