Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 390 · 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 2 written when you write all the numbers from 1 to 40? (a) 4 (b) 13 (c) 14 (d) 15
2. 2.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) 66 (b) 69 (c) 198 (d) 22
3. 3.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
4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 15 (b) 5 (c) 17 (d) 16
5. 5.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
6. 6.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
7. 7.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) 63 (d) 180
8. 8.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) 24 (b) 72 (c) 8 (d) 27
9. 9.The numbers 17 to 25 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 189 (b) 21 (c) 63 (d) 66
10. 10.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) 135 (b) 15 (c) 48 (d) 45
11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 17 (b) 16 (c) 15 (d) 6
12. 12.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
13. 13.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 5 (c) 7 (d) 10
14. 14.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 64 (c) 63 (d) 54
15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 13 (b) 3 (c) 14 (d) 12
16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 20 (b) 18 (c) 8 (d) 19
17. 17.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 285 (c) 262 (d) 286
18. 18.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
19. 19.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) 23 (b) 207 (c) 69 (d) 72
20. 20.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
21. 21.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) 133 (c) 134 (d) 124
22. 22.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 74? (a) 17 (b) 7 (c) 16 (d) 18
24. 24.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 220 (c) 210 (d) 218
25. 25.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 313 (b) 312 (c) 280 (d) 303
26. 26.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
27. 27.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 78 (c) 69 (d) 70
28. 28.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
29. 29.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) 54 (b) 17 (c) 153 (d) 51
30. 30.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 267 (c) 277 (d) 276
31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 14 (b) 16 (c) 4 (d) 15
32. 32.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
33. 33.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 17 (d) 18
34. 34.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 178 (c) 169 (d) 160
35. 35.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) 19 (b) 60 (c) 171 (d) 57
36. 36.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
37. 37.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 525 (c) 526 (d) 422
38. 38.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) 116 (c) 124 (d) 106
39. 39.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 404 (b) 489 (c) 498 (d) 499
40. 40.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 159 (b) 160 (c) 168 (d) 150

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