Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 118 · 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 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) 66 (d) 69
2. 2.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) 72 (b) 69 (c) 23 (d) 207
3. 3.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 9 (d) 11
4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 16 (b) 6 (c) 17 (d) 18
5. 5.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) 27 (b) 30 (c) 81 (d) 9
6. 6.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 459 (c) 460 (d) 378
7. 7.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 55 (c) 46 (d) 64
8. 8.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) 15 (b) 5 (c) 45 (d) 18
9. 9.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 588 (c) 579 (d) 464
10. 10.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) 90 (b) 33 (c) 10 (d) 30
11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 56? (a) 5 (b) 3 (c) 6 (d) 4
12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 18 (b) 17 (c) 16 (d) 6
13. 13.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 501 (b) 406 (c) 492 (d) 502
14. 14.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 102 (c) 84 (d) 93
15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 9 (d) 19
16. 16.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
17. 17.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) 24 (c) 27 (d) 72
18. 18.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
19. 19.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 573 (c) 460 (d) 583
20. 20.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 513 (c) 414 (d) 514
21. 21.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 504 (c) 495 (d) 505
22. 22.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 18 (b) 6 (c) 17 (d) 16
24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 5 (b) 3 (c) 4 (d) 2
25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 52? (a) 16 (b) 5 (c) 15 (d) 14
26. 26.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 85 (c) 76 (d) 94
27. 27.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
28. 28.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) 12 (d) 108
29. 29.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
30. 30.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 105 (b) 114 (c) 96 (d) 106
31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 15 (b) 13 (c) 14 (d) 3
32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 19 (b) 9 (c) 18 (d) 20
33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 16 (b) 15 (c) 14 (d) 4
34. 34.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 294 (c) 303 (d) 274
35. 35.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
36. 36.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 210 (c) 219 (d) 220
37. 37.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 342 (c) 396 (d) 405
38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 3 (b) 4 (c) 2 (d) 5
39. 39.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 210 (b) 201 (c) 211 (d) 212
40. 40.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) 54 (c) 18 (d) 57

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