Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 670 · 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 63? (a) 6 (b) 5 (c) 7 (d) 4
2. 2.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 3 (b) 5 (c) 2 (d) 4
4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 21 (d) 19
5. 5.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) 30 (b) 10 (c) 90 (d) 33
6. 6.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 567 (c) 577 (d) 576
7. 7.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) 18 (b) 15 (c) 5 (d) 45
8. 8.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 92 (c) 101 (d) 102
9. 9.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 38 (c) 28 (d) 46
10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 3 (b) 6 (c) 4 (d) 5
11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 64? (a) 4 (b) 5 (c) 7 (d) 6
12. 12.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 441 (c) 451 (d) 372
13. 13.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 268 (b) 295 (c) 294 (d) 285
14. 14.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) 16 (c) 48 (d) 144
15. 15.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) 72 (c) 207 (d) 23
16. 16.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
17. 17.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 48 (c) 58 (d) 57
18. 18.A book has 118 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 236 (c) 247 (d) 246
19. 19.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
20. 20.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
21. 21.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 158 (c) 157 (d) 148
22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 75? (a) 7 (b) 18 (c) 19 (d) 17
23. 23.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) 42 (b) 117 (c) 39 (d) 13
24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 16 (b) 5 (c) 15 (d) 17
25. 25.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 546 (c) 436 (d) 547
26. 26.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) 51 (b) 153 (c) 54 (d) 17
27. 27.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
28. 28.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
29. 29.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) 22 (c) 198 (d) 66
30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 21 (b) 19 (c) 20 (d) 9
31. 31.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 213 (c) 214 (d) 204
32. 32.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 97 (c) 98 (d) 106
33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 3 (b) 2 (c) 1 (d) 4
34. 34.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) 45 (b) 126 (c) 14 (d) 42
35. 35.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 3 (b) 4 (c) 5 (d) 6
37. 37.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) 27 (c) 81 (d) 30
38. 38.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 114 (c) 104 (d) 113
39. 39.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
40. 40.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6

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