Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 611 · 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.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 417 (c) 356 (d) 427
2. 2.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 14 (b) 15 (c) 4 (d) 13
4. 4.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) 54 (b) 51 (c) 153 (d) 17
5. 5.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 285 (c) 295 (d) 294
6. 6.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 72 (c) 71 (d) 80
7. 7.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
8. 8.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) 19 (b) 57 (c) 60 (d) 171
9. 9.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
10. 10.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 39 (b) 30 (c) 48 (d) 40
11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 20 (b) 9 (c) 19 (d) 21
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) 57 (c) 54 (d) 18
13. 13.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
14. 14.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 178 (c) 186 (d) 177
15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 73? (a) 18 (b) 17 (c) 7 (d) 16
16. 16.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 162 (c) 144 (d) 153
17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 18 (b) 16 (c) 7 (d) 17
18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 19 (d) 8
19. 19.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) 64 (c) 72 (d) 54
20. 20.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 109 (c) 118 (d) 100
21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 3 (b) 6 (c) 4 (d) 5
22. 22.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
23. 23.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
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) 108 (c) 36 (d) 39
25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 15 (b) 3 (c) 14 (d) 13
26. 26.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) 10 (c) 90 (d) 33
27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 6 (b) 7 (c) 4 (d) 5
28. 28.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 100 (c) 99 (d) 108
29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 18 (d) 20
30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 7 (d) 19
31. 31.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) 189 (b) 66 (c) 21 (d) 63
32. 32.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 222 (c) 232 (d) 226
33. 33.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
34. 34.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) 63 (d) 21
35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 5 (b) 17 (c) 16 (d) 15
36. 36.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) 20 (b) 63 (c) 60 (d) 180
37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 3 (b) 2 (c) 4 (d) 5
38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 15 (b) 13 (c) 14 (d) 3
39. 39.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) 22 (b) 198 (c) 69 (d) 66
40. 40.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 270 (c) 261 (d) 271

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