Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 548 · 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 11? (a) 9 (b) 12 (c) 8 (d) 7
2. 2.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 416 (b) 516 (c) 517 (d) 507
3. 3.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 534 (c) 543 (d) 544
4. 4.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) 44 (c) 53 (d) 62
5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 63? (a) 5 (b) 4 (c) 6 (d) 7
6. 6.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 248 (b) 264 (c) 265 (d) 255
7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 1 (c) 3 (d) 2
8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 4 (b) 1 (c) 2 (d) 3
9. 9.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 344 (b) 408 (c) 409 (d) 399
10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 1 (d) 2
11. 11.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 18 (b) 8 (c) 20 (d) 19
13. 13.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 391 (c) 390 (d) 332
14. 14.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 414 (c) 348 (d) 415
15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 17 (b) 7 (c) 18 (d) 16
16. 16.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 7 (b) 15 (c) 12 (d) 14
17. 17.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 84 (c) 92 (d) 83
18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 4 (b) 7 (c) 6 (d) 5
19. 19.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
20. 20.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) 30 (d) 90
21. 21.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) 18 (b) 6 (c) 21 (d) 54
22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 17 (d) 7
23. 23.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) 21 (b) 189 (c) 63 (d) 66
24. 24.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) 441 (c) 450 (d) 372
25. 25.A book has 180 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 433 (b) 423 (c) 360 (d) 432
26. 26.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 260 (b) 283 (c) 273 (d) 282
27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 7 (d) 16
28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 2 (b) 4 (c) 5 (d) 3
29. 29.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 7 (d) 17
31. 31.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
32. 32.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) 23 (c) 207 (d) 69
33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 19 (d) 17
34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 4 (b) 14 (c) 15 (d) 16
35. 35.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) 7 (d) 21
36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 15 (c) 4 (d) 16
37. 37.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 448 (c) 555 (d) 565
38. 38.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 336 (c) 337 (d) 327
39. 39.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 104 (c) 94 (d) 103
40. 40.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13

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