Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 905 · 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 9 written when you write all the numbers from 1 to 32? (a) 1 (b) 4 (c) 2 (d) 3
2. 2.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) 15 (c) 48 (d) 45
3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 2 (d) 3
4. 4.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) 57 (c) 54 (d) 18
5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 7 (b) 15 (c) 14 (d) 12
6. 6.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) 144 (b) 16 (c) 51 (d) 48
7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 1 (d) 3
8. 8.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 210 (c) 198 (d) 207
9. 9.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 4 (d) 5
11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 6 (b) 17 (c) 18 (d) 16
12. 12.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
13. 13.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) 18 (b) 5 (c) 15 (d) 45
14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 18 (b) 8 (c) 17 (d) 19
15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 5 (b) 7 (c) 8 (d) 4
16. 16.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 2 (b) 1 (c) 3 (d) 4
17. 17.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 330 (c) 340 (d) 339
18. 18.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
19. 19.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) 21 (b) 6 (c) 54 (d) 18
20. 20.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) 7 (c) 21 (d) 63
21. 21.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 124 (c) 133 (d) 142
22. 22.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
23. 23.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) 90 (b) 33 (c) 30 (d) 10
24. 24.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 304 (c) 349 (d) 348
25. 25.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 540 (c) 541 (d) 432
26. 26.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) 153 (b) 51 (c) 17 (d) 54
27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 6 (b) 4 (c) 3 (d) 5
28. 28.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 283 (c) 282 (d) 260
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) 72 (b) 27 (c) 8 (d) 24
30. 30.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 7 (b) 5 (c) 8 (d) 6
31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 5 (d) 2
32. 32.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
33. 33.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
34. 34.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 51 (b) 42 (c) 52 (d) 60
35. 35.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) 60 (c) 19 (d) 57
36. 36.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) 216 (c) 72 (d) 75
37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 3 (b) 15 (c) 14 (d) 13
38. 38.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 155 (b) 146 (c) 164 (d) 156
39. 39.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 15 (d) 4
40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 85? (a) 8 (b) 18 (c) 19 (d) 20

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