Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 833 · 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 times is the digit 8 written when you write all the numbers from 1 to 49? (a) 6 (b) 4 (c) 3 (d) 5
2. 2.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 10 (b) 12 (c) 11 (d) 9
4. 4.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) 14 (b) 42 (c) 45 (d) 126
5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 6 (b) 4 (c) 7 (d) 5
6. 6.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 417 (c) 408 (d) 350
7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 18 (b) 16 (c) 7 (d) 17
8. 8.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 339 (c) 340 (d) 330
9. 9.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) 39 (c) 117 (d) 42
10. 10.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 6 (b) 7 (c) 4 (d) 5
11. 11.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) 60 (c) 180 (d) 63
12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 3 (b) 5 (c) 4 (d) 6
13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 6 (b) 18 (c) 16 (d) 17
14. 14.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
15. 15.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 70 (c) 62 (d) 61
16. 16.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 441 (c) 451 (d) 450
17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 90? (a) 9 (b) 8 (c) 11 (d) 10
18. 18.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 156 (c) 147 (d) 138
19. 19.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
20. 20.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 14 (b) 15 (c) 3 (d) 13
22. 22.The numbers 11 to 19 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) 48 (c) 135 (d) 45
23. 23.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 318 (c) 369 (d) 360
24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 4 (b) 5 (c) 7 (d) 6
25. 25.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 585 (c) 595 (d) 594
26. 26.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) 216 (c) 72 (d) 75
27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 19 (d) 8
29. 29.A book has 126 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 270 (b) 271 (c) 252 (d) 261
30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 6 (b) 3 (c) 4 (d) 5
31. 31.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) 23 (c) 72 (d) 69
32. 32.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
33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 4 (b) 7 (c) 5 (d) 6
34. 34.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 2 (d) 18
35. 35.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 306 (b) 307 (c) 297 (d) 276
36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 4 (b) 6 (c) 5 (d) 3
37. 37.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) 11 (b) 36 (c) 33 (d) 99
38. 38.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
39. 39.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 482 (c) 606 (d) 616
40. 40.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 158 (c) 149 (d) 150

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