Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 577 · 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 4? (a) 5 (b) 4 (c) 3 (d) 10
2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 5 (b) 4 (c) 7 (d) 6
3. 3.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 157 (c) 148 (d) 158
4. 4.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) 189 (b) 21 (c) 66 (d) 63
5. 5.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
6. 6.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 56 (c) 55 (d) 64
7. 7.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 50 (c) 42 (d) 32
8. 8.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
9. 9.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 362 (c) 426 (d) 436
10. 10.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) 21 (b) 7 (c) 24 (d) 63
11. 11.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 475 (b) 388 (c) 474 (d) 465
12. 12.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 588 (c) 464 (d) 589
13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 9 (d) 18
14. 14.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 79 (b) 80 (c) 70 (d) 88
15. 15.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) 57 (b) 54 (c) 18 (d) 162
16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 3 (b) 5 (c) 2 (d) 4
17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 88? (a) 19 (b) 20 (c) 8 (d) 18
18. 18.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 296 (c) 336 (d) 337
19. 19.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 134 (c) 133 (d) 124
20. 20.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 7 (d) 5
21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 15 (b) 5 (c) 16 (d) 14
22. 22.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 84 (c) 66 (d) 75
23. 23.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 574 (c) 454 (d) 564
24. 24.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 266 (c) 282 (d) 291
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) 207 (d) 23
26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 68? (a) 6 (b) 16 (c) 17 (d) 18
27. 27.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 550 (c) 438 (d) 549
28. 28.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
29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 6 (b) 5 (c) 3 (d) 4
30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 2 (b) 5 (c) 4 (d) 3
31. 31.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) 72 (d) 8
32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 2 (b) 4 (c) 3 (d) 5
33. 33.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 17 (d) 3
34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 4 (b) 7 (c) 6 (d) 5
35. 35.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) 39 (b) 108 (c) 12 (d) 36
36. 36.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 507 (c) 416 (d) 517
37. 37.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) 171 (b) 19 (c) 57 (d) 60
38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 20 (d) 18
39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 18 (d) 7
40. 40.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) 483 (c) 400 (d) 493

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