Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 265 · 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.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 140 (c) 131 (d) 132
2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 17 (b) 16 (c) 18 (d) 6
3. 3.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
4. 4.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) 18 (c) 21 (d) 54
5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 54? (a) 16 (b) 15 (c) 5 (d) 17
6. 6.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 334 (b) 394 (c) 384 (d) 393
7. 7.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
8. 8.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 318 (c) 328 (d) 290
9. 9.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 591 (b) 592 (c) 466 (d) 582
10. 10.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 118 (c) 108 (d) 117
11. 11.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 201 (c) 192 (d) 206
12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 18 (d) 9
13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 88? (a) 18 (b) 17 (c) 19 (d) 8
14. 14.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 326 (c) 372 (d) 381
15. 15.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) 72 (c) 8 (d) 24
16. 16.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) 57 (b) 171 (c) 60 (d) 19
17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 19 (b) 20 (c) 8 (d) 18
18. 18.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 350 (b) 408 (c) 417 (d) 418
19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 4 (b) 6 (c) 3 (d) 5
20. 20.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
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) 133 (b) 134 (c) 142 (d) 124
22. 22.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 43? (a) 2 (b) 3 (c) 4 (d) 5
24. 24.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) 144 (d) 48
25. 25.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) 13 (b) 117 (c) 42 (d) 39
26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 76? (a) 17 (b) 18 (c) 19 (d) 7
27. 27.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
28. 28.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
29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 76? (a) 18 (b) 19 (c) 7 (d) 17
30. 30.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
31. 31.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 240 (c) 238 (d) 250
32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 19 (b) 7 (c) 17 (d) 18
33. 33.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 14 (d) 7
34. 34.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 48 (c) 39 (d) 30
35. 35.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 6 (b) 5 (c) 4 (d) 7
37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 6 (b) 16 (c) 17 (d) 18
38. 38.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 155 (c) 164 (d) 146
39. 39.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) 45 (c) 15 (d) 5
40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 1 (b) 4 (c) 2 (d) 3

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