Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 834 · 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 9 written when you write all the numbers from 1 to 70? (a) 6 (b) 8 (c) 5 (d) 7
2. 2.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
3. 3.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) 39 (c) 12 (d) 36
4. 4.The numbers 13 to 21 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 17 (b) 54 (c) 51 (d) 153
5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 15 (b) 4 (c) 14 (d) 16
6. 6.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) 60 (b) 180 (c) 20 (d) 63
7. 7.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
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) 207 (b) 23 (c) 69 (d) 72
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) 117 (b) 13 (c) 39 (d) 42
10. 10.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 2 (d) 1
11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 14 (b) 5 (c) 16 (d) 15
12. 12.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) 7 (c) 24 (d) 63
13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 64? (a) 18 (b) 16 (c) 17 (d) 6
14. 14.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 344 (c) 409 (d) 399
15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 18 (b) 6 (c) 16 (d) 17
16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 6 (b) 18 (c) 17 (d) 16
17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 6 (b) 8 (c) 7 (d) 5
18. 18.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) 6 (b) 54 (c) 21 (d) 18
19. 19.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 179 (b) 188 (c) 170 (d) 180
20. 20.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 580 (c) 579 (d) 570
21. 21.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 150 (c) 159 (d) 160
22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 6 (d) 5
23. 23.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 367 (c) 366 (d) 357
24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 73? (a) 18 (b) 17 (c) 7 (d) 19
25. 25.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) 10 (b) 30 (c) 90 (d) 33
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) 51 (b) 144 (c) 16 (d) 48
27. 27.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 460 (b) 378 (c) 459 (d) 450
28. 28.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) 42 (b) 126 (c) 45 (d) 14
29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 19 (b) 8 (c) 20 (d) 18
30. 30.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) 198 (d) 69
31. 31.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 4 (d) 3
32. 32.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
33. 33.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
34. 34.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 243 (b) 240 (c) 253 (d) 252
35. 35.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 438 (c) 364 (d) 439
36. 36.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 6 (d) 5
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) 33 (b) 99 (c) 11 (d) 36
38. 38.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) 72 (b) 24 (c) 75 (d) 216
39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 66? (a) 6 (b) 18 (c) 17 (d) 16
40. 40.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 537 (c) 547 (d) 546

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