Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 494 · 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.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 60 (c) 69 (d) 78
2. 2.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) 9 (b) 30 (c) 81 (d) 27
3. 3.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 108 (c) 116 (d) 107
4. 4.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) 24 (b) 8 (c) 72 (d) 27
5. 5.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) 23 (b) 207 (c) 69 (d) 72
6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 6 (b) 5 (c) 4 (d) 7
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) 42 (b) 41 (c) 50 (d) 32
8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 5 (b) 6 (c) 3 (d) 4
9. 9.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
10. 10.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 17 (b) 5 (c) 15 (d) 16
12. 12.The numbers 20 to 28 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) 75 (c) 72 (d) 216
13. 13.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 392 (b) 471 (c) 481 (d) 480
14. 14.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
15. 15.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 64 (c) 73 (d) 82
16. 16.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 40 (c) 58 (d) 49
17. 17.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
18. 18.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) 57 (d) 18
19. 19.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 318 (c) 290 (d) 328
20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 3 (b) 5 (c) 4 (d) 6
21. 21.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) 18 (d) 5
22. 22.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) 180 (b) 20 (c) 63 (d) 60
23. 23.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) 144 (c) 48 (d) 51
24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 16 (d) 17
25. 25.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) 36 (d) 12
26. 26.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) 124 (d) 133
27. 27.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
28. 28.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) 22 (c) 69 (d) 66
29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 1 (b) 2 (c) 4 (d) 3
30. 30.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 22 (c) 31 (d) 40
31. 31.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 444 (c) 453 (d) 374
32. 32.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) 44 (c) 43 (d) 34
33. 33.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 16 (d) 4
34. 34.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
35. 35.How many times is the digit 4 written when you write all the numbers from 1 to 32? (a) 2 (b) 3 (c) 4 (d) 1
36. 36.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
37. 37.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) 54 (c) 153 (d) 17
38. 38.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) 14 (b) 45 (c) 42 (d) 126
39. 39.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 448 (c) 447 (d) 438
40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 13 (b) 15 (c) 3 (d) 14

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