Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 11 · 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 8? (a) 7 (b) 9 (c) 10 (d) 8
2. 2.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 20 (b) 19 (c) 21 (d) 9
4. 4.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) 144 (c) 153 (d) 162
5. 5.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 72 (c) 81 (d) 90
6. 6.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 112 (c) 120 (d) 111
7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 13 (b) 14 (c) 15 (d) 4
8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 2 (d) 5
9. 9.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 223 (c) 220 (d) 213
10. 10.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 573 (c) 460 (d) 583
11. 11.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 592 (c) 591 (d) 466
12. 12.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) 117 (b) 13 (c) 42 (d) 39
13. 13.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 4 (d) 5
14. 14.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 213 (b) 321 (c) 214 (d) 204
15. 15.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 84 (c) 102 (d) 93
16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 15 (d) 16
17. 17.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 34 (c) 44 (d) 43
18. 18.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
19. 19.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 139 (c) 130 (d) 140
20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 19 (b) 20 (c) 9 (d) 18
21. 21.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) 15 (c) 18 (d) 5
22. 22.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) 72 (b) 216 (c) 24 (d) 75
23. 23.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) 135 (c) 45 (d) 15
24. 24.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 352 (b) 421 (c) 411 (d) 420
25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 3 (d) 1
26. 26.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
27. 27.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 457 (b) 447 (c) 376 (d) 456
28. 28.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) 17 (d) 153
29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 7 (d) 19
30. 30.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 487 (c) 486 (d) 477
31. 31.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 465 (b) 388 (c) 475 (d) 474
32. 32.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
33. 33.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) 72 (b) 27 (c) 24 (d) 8
34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 16 (b) 18 (c) 7 (d) 17
35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 18 (b) 6 (c) 16 (d) 17
36. 36.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) 54 (c) 18 (d) 21
37. 37.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 424 (c) 354 (d) 423
38. 38.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
39. 39.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 501 (c) 511 (d) 412
40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 7 (d) 18

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