Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 352 · 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 89? (a) 19 (b) 8 (c) 18 (d) 20
2. 2.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 153 (c) 144 (d) 162
3. 3.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 249 (c) 258 (d) 259
4. 4.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 1 (b) 3 (c) 4 (d) 2
6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 15 (b) 17 (c) 16 (d) 5
7. 7.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) 27 (b) 24 (c) 8 (d) 72
8. 8.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 22 (c) 31 (d) 40
9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 18 (d) 8
10. 10.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) 33 (b) 99 (c) 36 (d) 11
11. 11.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 62 (c) 70 (d) 61
12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 20 (b) 9 (c) 18 (d) 19
13. 13.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
14. 14.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 220 (c) 210 (d) 218
15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 5 (b) 6 (c) 3 (d) 4
16. 16.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 95? (a) 21 (b) 20 (c) 9 (d) 19
18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 6 (b) 17 (c) 16 (d) 15
19. 19.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 42 (c) 32 (d) 41
20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 16 (b) 5 (c) 15 (d) 17
21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 17 (b) 6 (c) 18 (d) 16
22. 22.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 465 (c) 466 (d) 456
23. 23.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 75 (c) 84 (d) 76
24. 24.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
25. 25.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 301 (c) 272 (d) 291
26. 26.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 573 (c) 582 (d) 583
27. 27.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) 171 (c) 60 (d) 57
28. 28.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 247 (c) 236 (d) 237
29. 29.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 513 (c) 514 (d) 414
30. 30.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 79 (c) 88 (d) 70
31. 31.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 21 (c) 189 (d) 63
32. 32.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) 54 (b) 51 (c) 153 (d) 17
33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 14 (b) 3 (c) 15 (d) 13
34. 34.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) 63 (c) 21 (d) 7
35. 35.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) 22 (c) 198 (d) 66
36. 36.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 372 (c) 381 (d) 326
37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 2 (d) 4
38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 44? (a) 4 (b) 5 (c) 3 (d) 2
39. 39.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) 60 (b) 63 (c) 20 (d) 180
40. 40.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 199 (b) 189 (c) 198 (d) 204

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