Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 487 · 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 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 3 (c) 10 (d) 9
2. 2.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
3. 3.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
4. 4.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) 132 (c) 122 (d) 131
5. 5.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 130 (c) 112 (d) 121
6. 6.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 160 (c) 169 (d) 178
7. 7.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
8. 8.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
9. 9.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 451 (b) 450 (c) 372 (d) 441
10. 10.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 4 (d) 5
12. 12.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 390 (c) 477 (d) 468
13. 13.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 586 (c) 576 (d) 462
14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 18 (b) 19 (c) 17 (d) 7
15. 15.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 559 (c) 444 (d) 558
16. 16.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 36 (b) 39 (c) 12 (d) 108
17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 19 (d) 20
18. 18.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 316 (c) 282 (d) 315
19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 17 (d) 19
20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 4 (b) 5 (c) 2 (d) 3
21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 18 (d) 8
22. 22.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 448 (c) 565 (d) 564
23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 15 (b) 13 (c) 14 (d) 3
24. 24.The numbers 12 to 20 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) 51 (c) 16 (d) 144
25. 25.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) 72 (b) 69 (c) 23 (d) 207
26. 26.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
27. 27.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) 18 (b) 45 (c) 5 (d) 15
28. 28.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 78 (c) 88 (d) 87
29. 29.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) 466 (c) 456 (d) 465
30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 4 (d) 16
31. 31.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 493 (c) 483 (d) 400
32. 32.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) 54 (b) 162 (c) 18 (d) 57
33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 20 (b) 18 (c) 9 (d) 19
34. 34.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 494 (b) 634 (c) 624 (d) 633
35. 35.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 391 (b) 381 (c) 390 (d) 332
36. 36.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 366 (c) 357 (d) 316
37. 37.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 187 (b) 188 (c) 196 (d) 178
38. 38.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) 9 (d) 27
39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 3 (b) 12 (c) 11 (d) 10
40. 40.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) 198 (b) 66 (c) 22 (d) 69

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