Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 349 · 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.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 19 (d) 18
3. 3.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 60 (c) 59 (d) 50
4. 4.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) 108 (b) 12 (c) 39 (d) 36
5. 5.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) 63 (b) 180 (c) 60 (d) 20
6. 6.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 321 (c) 331 (d) 292
7. 7.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) 57 (b) 60 (c) 19 (d) 171
8. 8.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
9. 9.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
10. 10.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 387 (c) 397 (d) 396
11. 11.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 177 (c) 186 (d) 168
12. 12.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
13. 13.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 333 (c) 342 (d) 343
14. 14.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) 18 (c) 57 (d) 162
15. 15.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 513 (c) 523 (d) 420
16. 16.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 90 (c) 72 (d) 82
17. 17.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 89 (c) 80 (d) 98
18. 18.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) 15 (d) 18
19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 20 (d) 9
20. 20.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 349 (c) 339 (d) 348
21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 7 (b) 6 (c) 8 (d) 9
22. 22.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 10 (d) 7
23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 87? (a) 9 (b) 6 (c) 7 (d) 8
24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 17 (b) 8 (c) 19 (d) 18
25. 25.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
26. 26.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 116 (c) 126 (d) 125
27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 5 (b) 15 (c) 17 (d) 16
28. 28.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) 207 (b) 69 (c) 23 (d) 72
29. 29.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 91 (c) 82 (d) 92
30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 19 (b) 18 (c) 17 (d) 8
31. 31.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 463 (b) 380 (c) 453 (d) 462
32. 32.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) 69 (b) 66 (c) 22 (d) 198
33. 33.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 631 (b) 630 (c) 621 (d) 492
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) 21 (c) 63 (d) 7
35. 35.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
36. 36.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 408 (c) 505 (d) 504
37. 37.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) 21 (b) 6 (c) 54 (d) 18
38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 15 (c) 14 (d) 13
39. 39.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
40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 9 (d) 18

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