Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 582 · 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 6 written when you write all the numbers from 1 to 74? (a) 7 (b) 17 (c) 16 (d) 18
2. 2.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 13 (b) 14 (c) 15 (d) 3
4. 4.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) 45 (c) 5 (d) 18
5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 2 (d) 1
6. 6.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) 27 (b) 8 (c) 24 (d) 72
7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 7 (b) 17 (c) 18 (d) 19
8. 8.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) 72 (d) 207
9. 9.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 14 (d) 15
11. 11.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
12. 12.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 240 (c) 249 (d) 238
13. 13.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 66 (c) 76 (d) 84
14. 14.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 547 (b) 546 (c) 436 (d) 537
15. 15.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 40 (c) 30 (d) 39
16. 16.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 7 (d) 6
17. 17.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 481 (b) 480 (c) 471 (d) 392
18. 18.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 208 (c) 195 (d) 205
19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 70? (a) 8 (b) 5 (c) 6 (d) 7
20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 20 (d) 9
21. 21.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 255 (c) 242 (d) 256
22. 22.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 343 (b) 300 (c) 333 (d) 342
23. 23.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 134 (c) 133 (d) 124
24. 24.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 4 (d) 6
25. 25.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 268 (c) 250 (d) 267
26. 26.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) 16 (c) 51 (d) 48
27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 8 (b) 6 (c) 7 (d) 9
28. 28.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 387 (c) 330 (d) 388
29. 29.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) 9 (b) 81 (c) 30 (d) 27
30. 30.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 104 (c) 95 (d) 86
31. 31.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 272 (c) 300 (d) 301
32. 32.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) 7 (c) 21 (d) 63
33. 33.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) 66 (c) 69 (d) 198
34. 34.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 173 (c) 164 (d) 182
35. 35.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
36. 36.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
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) 18 (c) 54 (d) 6
38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 2 (b) 4 (c) 1 (d) 3
39. 39.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 18 (b) 7 (c) 19 (d) 17

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