Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 865 · 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 4 written when you write all the numbers from 1 to 60? (a) 17 (b) 15 (c) 16 (d) 6
2. 2.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) 189 (c) 66 (d) 63
3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 16 (d) 17
4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 16 (b) 14 (c) 4 (d) 15
5. 5.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
6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 20 (b) 18 (c) 8 (d) 19
7. 7.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 13 (b) 14 (c) 15 (d) 4
9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 6 (b) 7 (c) 8 (d) 5
10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 9 (d) 19
11. 11.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 231 (c) 241 (d) 240
12. 12.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 255 (c) 248 (d) 265
13. 13.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 216 (c) 225 (d) 222
14. 14.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) 153 (c) 51 (d) 54
15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 16 (b) 15 (c) 17 (d) 5
16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 16 (b) 5 (c) 14 (d) 15
17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 7 (b) 6 (c) 8 (d) 9
18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 81? (a) 17 (b) 18 (c) 8 (d) 19
19. 19.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) 30 (b) 9 (c) 27 (d) 81
20. 20.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 543 (c) 544 (d) 534
21. 21.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) 57 (b) 54 (c) 162 (d) 18
22. 22.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 3 (d) 1
24. 24.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) 12 (b) 36 (c) 108 (d) 39
25. 25.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 627 (c) 628 (d) 490
26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 4 (b) 13 (c) 14 (d) 15
27. 27.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 140 (c) 130 (d) 148
28. 28.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) 57 (d) 19
29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 16 (b) 17 (c) 7 (d) 18
30. 30.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 6 (b) 5 (c) 8 (d) 7
32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 16 (b) 6 (c) 17 (d) 18
33. 33.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) 30 (b) 90 (c) 33 (d) 10
34. 34.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
35. 35.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 109 (c) 110 (d) 100
36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 12 (b) 3 (c) 10 (d) 11
37. 37.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 68 (c) 59 (d) 60
38. 38.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) 48 (c) 51 (d) 16
39. 39.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 396 (c) 486 (d) 487
40. 40.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) 15 (c) 18 (d) 45

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad