Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 53 · 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 67? (a) 6 (b) 7 (c) 4 (d) 5
2. 2.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
3. 3.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 529 (b) 424 (c) 528 (d) 519
4. 4.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) 27 (d) 30
5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 4 (b) 3 (c) 5 (d) 2
6. 6.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 484 (c) 394 (d) 483
7. 7.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 310 (c) 357 (d) 358
8. 8.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) 60 (b) 19 (c) 171 (d) 57
9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 19 (b) 17 (c) 18 (d) 8
10. 10.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) 24 (c) 72 (d) 8
11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 16 (d) 5
12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 5 (b) 6 (c) 3 (d) 4
13. 13.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
14. 14.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
15. 15.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) 126 (c) 42 (d) 45
16. 16.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 10 (d) 8
17. 17.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
18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 2 (d) 1
19. 19.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) 30 (c) 40 (d) 39
20. 20.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 505 (c) 408 (d) 495
21. 21.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
22. 22.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) 18 (c) 5 (d) 15
23. 23.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 15 (b) 14 (c) 4 (d) 16
25. 25.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
26. 26.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
27. 27.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) 33 (b) 10 (c) 30 (d) 90
28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 21 (d) 9
29. 29.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 140 (b) 130 (c) 148 (d) 139
30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 4 (b) 8 (c) 7 (d) 5
31. 31.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 223 (b) 213 (c) 220 (d) 222
32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 19 (b) 17 (c) 18 (d) 8
33. 33.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 3 (d) 17
34. 34.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 9 (c) 3 (d) 10
35. 35.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 158 (c) 166 (d) 148
36. 36.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 115 (b) 106 (c) 116 (d) 124
37. 37.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 597 (b) 476 (c) 607 (d) 606
38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 3 (b) 2 (c) 1 (d) 4
39. 39.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) 135 (c) 48 (d) 45
40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 91? (a) 18 (b) 19 (c) 9 (d) 20

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