Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 454 · 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 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) 21 (b) 24 (c) 7 (d) 63
2. 2.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 83 (b) 84 (c) 92 (d) 74
3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 12 (b) 9 (c) 7 (d) 11
4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 5 (b) 16 (c) 14 (d) 15
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) 126 (b) 45 (c) 14 (d) 42
6. 6.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) 24 (b) 72 (c) 216 (d) 75
7. 7.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 394 (c) 484 (d) 483
8. 8.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 4 (b) 15 (c) 14 (d) 13
10. 10.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 192 (c) 200 (d) 183
11. 11.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) 69 (b) 23 (c) 207 (d) 72
12. 12.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) 60 (b) 57 (c) 171 (d) 19
13. 13.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 312 (c) 321 (d) 322
14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 16 (b) 6 (c) 18 (d) 17
15. 15.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 376 (c) 322 (d) 375
16. 16.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
17. 17.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) 180 (d) 60
18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 2 (b) 4 (c) 3 (d) 5
19. 19.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 19 (d) 9
21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 19 (b) 18 (c) 17 (d) 8
22. 22.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 310 (c) 358 (d) 357
23. 23.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) 69 (c) 198 (d) 66
24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 9 (b) 18 (c) 20 (d) 19
25. 25.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 6 (b) 3 (c) 7 (d) 4
27. 27.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) 24 (b) 8 (c) 27 (d) 72
28. 28.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 3 (b) 2 (c) 4 (d) 5
30. 30.A book has 153 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 306 (c) 352 (d) 342
31. 31.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 78 (c) 69 (d) 60
32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 6 (b) 7 (c) 5 (d) 8
33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 16 (b) 15 (c) 4 (d) 14
34. 34.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 19 (b) 17 (c) 7 (d) 18
36. 36.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
37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 17 (b) 18 (c) 16 (d) 6
38. 38.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 440 (c) 552 (d) 553
39. 39.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) 63 (d) 21
40. 40.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 600 (c) 601 (d) 472

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