Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 378 · 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 42? (a) 16 (b) 15 (c) 14 (d) 4
2. 2.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
3. 3.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
4. 4.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 136 (c) 145 (d) 146
5. 5.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
6. 6.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
7. 7.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) 8 (b) 72 (c) 24 (d) 27
8. 8.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
9. 9.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) 108 (b) 39 (c) 12 (d) 36
10. 10.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) 72 (d) 69
11. 11.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 618 (c) 627 (d) 628
12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 17 (b) 8 (c) 18 (d) 19
13. 13.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) 22 (c) 66 (d) 198
14. 14.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 6 (d) 5
15. 15.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 19 (b) 18 (c) 7 (d) 17
17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 18 (b) 17 (c) 19 (d) 7
18. 18.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) 10 (c) 30 (d) 33
19. 19.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) 63 (b) 189 (c) 21 (d) 66
20. 20.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 63 (b) 54 (c) 64 (d) 72
21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 9 (b) 19 (c) 18 (d) 20
22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 33? (a) 3 (b) 13 (c) 14 (d) 15
23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 17 (b) 5 (c) 15 (d) 16
24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 3 (b) 15 (c) 14 (d) 13
25. 25.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 291 (c) 300 (d) 272
26. 26.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 114 (c) 105 (d) 106
27. 27.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 481 (b) 471 (c) 480 (d) 392
28. 28.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) 17 (b) 54 (c) 51 (d) 153
29. 29.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 546 (c) 436 (d) 547
30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 16 (b) 4 (c) 14 (d) 15
31. 31.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 278 (b) 310 (c) 300 (d) 309
32. 32.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) 27 (d) 81
33. 33.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 16 (b) 14 (c) 15 (d) 4
35. 35.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
36. 36.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) 51 (c) 48 (d) 16
37. 37.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 18 (d) 17
39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 19 (b) 18 (c) 7 (d) 17
40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 5 (b) 4 (c) 7 (d) 6

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