Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 332 · 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) 3 (b) 4 (c) 10 (d) 5
2. 2.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
3. 3.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) 36 (b) 11 (c) 99 (d) 33
4. 4.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 570 (c) 579 (d) 458
5. 5.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 7 (d) 18
7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 4 (b) 5 (c) 6 (d) 3
8. 8.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 8 (b) 10 (c) 11 (d) 9
10. 10.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 45 (b) 54 (c) 46 (d) 36
11. 11.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) 207 (b) 23 (c) 72 (d) 69
12. 12.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) 54 (c) 57 (d) 18
13. 13.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) 54 (c) 6 (d) 21
14. 14.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) 60 (b) 20 (c) 63 (d) 180
15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 4 (d) 5
16. 16.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 10 (b) 11 (c) 8 (d) 9
18. 18.A book has 215 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 430 (c) 538 (d) 537
19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 5 (b) 6 (c) 4 (d) 3
20. 20.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
21. 21.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 19 (b) 18 (c) 20 (d) 9
22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 16 (b) 17 (c) 7 (d) 18
23. 23.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) 57 (c) 19 (d) 60
24. 24.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 315 (b) 325 (c) 288 (d) 324
25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 13 (b) 15 (c) 3 (d) 14
26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 12 (b) 10 (c) 7 (d) 13
27. 27.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 51 (c) 52 (d) 42
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) 16 (b) 51 (c) 48 (d) 144
29. 29.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) 21 (b) 63 (c) 189 (d) 66
30. 30.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 397 (c) 396 (d) 336
31. 31.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) 33 (b) 10 (c) 30 (d) 90
32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 3 (b) 5 (c) 6 (d) 4
33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 15 (b) 17 (c) 16 (d) 5
34. 34.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) 54 (c) 17 (d) 51
35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 11 (b) 10 (c) 3 (d) 12
36. 36.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 84 (c) 93 (d) 102
37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 84? (a) 18 (b) 20 (c) 8 (d) 19
38. 38.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) 45 (c) 5 (d) 15
39. 39.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 135 (c) 126 (d) 136
40. 40.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) 69 (b) 198 (c) 22 (d) 66

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