Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 364 · 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 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) 207 (c) 69 (d) 23
2. 2.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 453 (b) 454 (c) 374 (d) 444
3. 3.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 68 (c) 78 (d) 77
4. 4.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
5. 5.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 107 (c) 98 (d) 116
6. 6.The numbers 10 to 18 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) 42 (c) 126 (d) 14
7. 7.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) 51 (b) 153 (c) 54 (d) 17
8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 4 (b) 15 (c) 13 (d) 14
9. 9.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 13 (b) 15 (c) 3 (d) 14
11. 11.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 22 (b) 32 (c) 31 (d) 40
12. 12.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 396 (c) 486 (d) 477
13. 13.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) 16 (b) 51 (c) 48 (d) 144
14. 14.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 368 (b) 445 (c) 444 (d) 435
15. 15.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 481 (c) 392 (d) 480
16. 16.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) 135 (b) 45 (c) 15 (d) 48
17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 6 (b) 16 (c) 15 (d) 17
18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 17 (d) 8
19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 2 (d) 1
20. 20.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) 63 (b) 180 (c) 20 (d) 60
21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 17 (b) 7 (c) 18 (d) 19
22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 18 (b) 8 (c) 19 (d) 20
23. 23.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 94 (c) 76 (d) 85
24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 47? (a) 3 (b) 6 (c) 4 (d) 5
25. 25.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) 162 (b) 18 (c) 57 (d) 54
26. 26.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) 5 (d) 18
27. 27.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) 88 (c) 70 (d) 80
28. 28.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 490 (c) 628 (d) 627
29. 29.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) 8 (c) 24 (d) 72
30. 30.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
31. 31.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
32. 32.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 351 (c) 306 (d) 352
33. 33.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 17 (d) 2
34. 34.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 163 (b) 164 (c) 154 (d) 172
35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 7 (b) 5 (c) 6 (d) 4
36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 6 (b) 17 (c) 18 (d) 16
37. 37.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
38. 38.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 111 (c) 120 (d) 102
39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 5 (b) 6 (c) 4 (d) 3
40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 14 (b) 15 (c) 16 (d) 4

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