Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 441 · 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 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 640 (b) 498 (c) 639 (d) 630
2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 16 (b) 17 (c) 6 (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) 60 (b) 63 (c) 180 (d) 20
4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 18 (b) 17 (c) 7 (d) 19
5. 5.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 45 (b) 14 (c) 42 (d) 126
6. 6.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
7. 7.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 2 (c) 17 (d) 4
8. 8.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) 81 (d) 27
9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 5 (b) 14 (c) 16 (d) 15
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) 69 (d) 72
11. 11.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 15 (d) 5
12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 18 (d) 17
13. 13.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) 72 (b) 75 (c) 216 (d) 24
14. 14.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) 21 (c) 63 (d) 66
15. 15.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) 6 (b) 18 (c) 54 (d) 21
16. 16.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 74? (a) 6 (b) 8 (c) 7 (d) 5
18. 18.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 451 (b) 441 (c) 450 (d) 372
19. 19.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) 17 (c) 51 (d) 54
20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 20 (b) 8 (c) 18 (d) 19
21. 21.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 46 (b) 56 (c) 64 (d) 55
22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 4 (b) 11 (c) 10 (d) 12
23. 23.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 90 (c) 72 (d) 81
24. 24.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 42 (c) 117 (d) 39
25. 25.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 73 (c) 64 (d) 82
26. 26.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) 336 (c) 396 (d) 397
27. 27.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 314 (c) 364 (d) 363
28. 28.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 7 (d) 10
29. 29.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
30. 30.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
31. 31.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 552 (c) 561 (d) 446
32. 32.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 309 (c) 278 (d) 300
33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 14 (b) 13 (c) 15 (d) 3
34. 34.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) 10 (d) 33
35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 44? (a) 5 (b) 4 (c) 2 (d) 3
36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 13 (b) 10 (c) 12 (d) 9
37. 37.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 279 (c) 289 (d) 288
38. 38.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 634 (c) 624 (d) 494
39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 45? (a) 14 (b) 16 (c) 4 (d) 15
40. 40.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 173 (c) 182 (d) 174

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