Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 79 · 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 two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
2. 2.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) 72 (d) 69
3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 69? (a) 17 (b) 16 (c) 6 (d) 18
4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 10 (b) 3 (c) 8 (d) 9
5. 5.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
6. 6.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 528 (c) 529 (d) 519
7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 90? (a) 18 (b) 19 (c) 9 (d) 20
8. 8.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 423 (c) 424 (d) 414
9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 55? (a) 3 (b) 6 (c) 4 (d) 5
10. 10.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 10 (d) 9
11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 2 (b) 3 (c) 1 (d) 4
12. 12.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) 15 (c) 135 (d) 48
13. 13.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 94 (c) 103 (d) 104
14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 16 (d) 17
15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 5 (d) 6
16. 16.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 637 (c) 636 (d) 496
17. 17.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
18. 18.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) 13 (c) 42 (d) 117
19. 19.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 19 (b) 18 (c) 7 (d) 17
21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 4 (b) 2 (c) 1 (d) 3
22. 22.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) 134 (c) 142 (d) 124
23. 23.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 35 (b) 36 (c) 44 (d) 26
24. 24.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 157 (c) 148 (d) 166
25. 25.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 96 (c) 105 (d) 114
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) 11 (b) 99 (c) 36 (d) 33
27. 27.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 238 (c) 240 (d) 249
28. 28.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) 5 (b) 18 (c) 45 (d) 15
29. 29.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) 176 (c) 186 (d) 194
30. 30.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) 24 (b) 75 (c) 216 (d) 72
31. 31.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 6 (b) 3 (c) 5 (d) 4
33. 33.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 201 (c) 210 (d) 211
34. 34.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
35. 35.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
36. 36.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 277 (c) 267 (d) 276
37. 37.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 139 (c) 140 (d) 148
38. 38.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) 18 (b) 162 (c) 57 (d) 54
39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 4 (d) 5
40. 40.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8

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