Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 999 · 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 9 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 2 (d) 3
2. 2.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 158 (c) 167 (d) 168
3. 3.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 402 (c) 403 (d) 393
4. 4.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
5. 5.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) 57 (c) 171 (d) 19
6. 6.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
7. 7.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
8. 8.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 53 (c) 62 (d) 44
9. 9.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 358 (c) 310 (d) 357
10. 10.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 16 (b) 17 (c) 6 (d) 18
12. 12.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 130 (c) 129 (d) 138
13. 13.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 131 (c) 132 (d) 122
14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 1 (b) 3 (c) 4 (d) 2
15. 15.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) 338 (c) 400 (d) 399
16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 17 (b) 18 (c) 6 (d) 16
17. 17.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 256 (c) 267 (d) 277
18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 7 (b) 19 (c) 17 (d) 18
19. 19.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) 48 (b) 15 (c) 135 (d) 45
20. 20.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
21. 21.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) 24 (b) 21 (c) 63 (d) 7
22. 22.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 33 (b) 24 (c) 42 (d) 34
23. 23.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) 54 (c) 162 (d) 18
24. 24.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
25. 25.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 289 (b) 279 (c) 264 (d) 288
26. 26.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 420 (c) 352 (d) 411
27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 5 (b) 6 (c) 8 (d) 7
28. 28.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) 30 (b) 9 (c) 27 (d) 81
29. 29.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
30. 30.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 196 (c) 187 (d) 178
31. 31.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 166 (c) 157 (d) 158
32. 32.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 306 (c) 315 (d) 282
33. 33.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
34. 34.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) 72 (d) 24
35. 35.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 43 (c) 52 (d) 34
36. 36.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
37. 37.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
38. 38.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 96 (c) 88 (d) 87
39. 39.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) 54 (b) 6 (c) 21 (d) 18
40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 7 (b) 19 (c) 17 (d) 18

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