Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 436 · 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.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) 42 (b) 14 (c) 45 (d) 126
2. 2.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) 63 (c) 7 (d) 21
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) 33 (b) 11 (c) 99 (d) 36
4. 4.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 6 (b) 8 (c) 4 (d) 9
6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 5 (b) 7 (c) 4 (d) 6
7. 7.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 60 (c) 42 (d) 51
8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 17 (c) 6 (d) 16
9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 18 (d) 19
10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 14 (b) 4 (c) 15 (d) 16
11. 11.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) 16 (d) 48
12. 12.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 236 (c) 247 (d) 237
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) 6 (c) 21 (d) 54
14. 14.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 458 (c) 580 (d) 579
15. 15.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
16. 16.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 571 (c) 452 (d) 561
17. 17.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 104 (c) 94 (d) 103
18. 18.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
19. 19.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 172 (c) 171 (d) 180
20. 20.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 424 (c) 354 (d) 414
21. 21.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
22. 22.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
23. 23.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) 39 (b) 36 (c) 108 (d) 12
24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 6 (b) 4 (c) 5 (d) 3
25. 25.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
26. 26.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 366 (c) 357 (d) 316
27. 27.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 10 (b) 11 (c) 3 (d) 9
29. 29.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) 27 (c) 72 (d) 24
30. 30.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 38 (c) 47 (d) 48
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) 66 (b) 189 (c) 21 (d) 63
32. 32.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) 54 (b) 57 (c) 18 (d) 162
33. 33.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
34. 34.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) 180 (d) 63
35. 35.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) 45 (b) 5 (c) 18 (d) 15
36. 36.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
37. 37.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 241 (b) 231 (c) 232 (d) 240
38. 38.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 116 (c) 124 (d) 115
39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 4 (b) 16 (c) 14 (d) 15
40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 2 (b) 3 (c) 4 (d) 5

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