Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 969 · 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 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) 81 (c) 27 (d) 9
2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 19 (d) 18
3. 3.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 10 (b) 33 (c) 90 (d) 30
4. 4.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
5. 5.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 464 (c) 588 (d) 579
6. 6.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 5 (d) 16
7. 7.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 42 (c) 60 (d) 51
8. 8.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 213 (c) 220 (d) 222
9. 9.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) 24 (c) 27 (d) 8
10. 10.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) 57 (b) 171 (c) 60 (d) 19
11. 11.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 72 (c) 71 (d) 80
12. 12.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 8 (d) 11
13. 13.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 141 (c) 132 (d) 142
14. 14.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 212 (c) 201 (d) 211
15. 15.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 459 (c) 468 (d) 469
16. 16.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) 39 (d) 42
17. 17.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) 153 (b) 54 (c) 51 (d) 17
18. 18.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 93 (c) 94 (d) 102
19. 19.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 7 (b) 4 (c) 5 (d) 6
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) 63 (b) 24 (c) 7 (d) 21
22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 6 (d) 3
23. 23.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 117 (b) 126 (c) 118 (d) 108
24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 19 (d) 18
25. 25.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 571 (c) 452 (d) 570
26. 26.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 210 (c) 219 (d) 220
27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 21 (b) 9 (c) 19 (d) 20
28. 28.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) 456 (c) 465 (d) 466
29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 80? (a) 9 (b) 7 (c) 6 (d) 8
30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 8 (b) 20 (c) 19 (d) 18
31. 31.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) 20 (b) 63 (c) 180 (d) 60
32. 32.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 477 (c) 478 (d) 390
33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 15 (b) 13 (c) 14 (d) 3
34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 5 (b) 6 (c) 4 (d) 3
35. 35.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 7 (c) 8 (d) 10
36. 36.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 588 (c) 470 (d) 598
37. 37.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) 21 (d) 18
38. 38.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) 178 (c) 187 (d) 196
39. 39.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 16 (b) 15 (c) 14 (d) 5

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