Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 991 · 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 2 written when you write all the numbers from 1 to 79? (a) 18 (b) 17 (c) 7 (d) 19
2. 2.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 210 (c) 201 (d) 212
3. 3.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) 15 (b) 48 (c) 135 (d) 45
4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 7 (d) 17
5. 5.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
6. 6.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
7. 7.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) 90 (c) 30 (d) 33
8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 7 (b) 17 (c) 18 (d) 16
9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 18 (b) 16 (c) 6 (d) 17
10. 10.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) 18 (b) 162 (c) 54 (d) 57
11. 11.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 6 (d) 5
12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 17 (b) 16 (c) 6 (d) 18
13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 17 (b) 7 (c) 18 (d) 19
14. 14.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 342 (c) 406 (d) 396
15. 15.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
16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 16 (d) 15
17. 17.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
18. 18.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) 42 (b) 45 (c) 126 (d) 14
19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 55? (a) 17 (b) 5 (c) 15 (d) 16
20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 19 (d) 20
21. 21.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 48 (c) 58 (d) 57
22. 22.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 340 (c) 403 (d) 393
23. 23.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) 5 (b) 45 (c) 15 (d) 18
24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 19 (b) 18 (c) 17 (d) 8
25. 25.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
26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 10 (b) 8 (c) 9 (d) 7
27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 16 (b) 5 (c) 17 (d) 15
28. 28.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 223 (c) 213 (d) 220
29. 29.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 36 (d) 33
30. 30.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 114 (c) 105 (d) 96
31. 31.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 39 (c) 13 (d) 117
32. 32.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 424 (c) 423 (d) 414
33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 4 (b) 5 (c) 7 (d) 6
34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 19 (d) 8
35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 6 (b) 5 (c) 8 (d) 7
36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 19 (b) 17 (c) 7 (d) 18
37. 37.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
38. 38.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) 36 (c) 108 (d) 12
39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 19 (b) 17 (c) 7 (d) 18
40. 40.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 232 (c) 241 (d) 231

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