Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 840 · 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 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 151 (b) 160 (c) 152 (d) 142
2. 2.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
3. 3.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 91 (b) 82 (c) 100 (d) 92
4. 4.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) 63 (c) 66 (d) 21
5. 5.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) 42 (c) 13 (d) 39
6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 15 (b) 3 (c) 13 (d) 14
7. 7.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 12 (d) 8
8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 16 (b) 17 (c) 6 (d) 18
9. 9.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
10. 10.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
11. 11.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) 75 (b) 24 (c) 216 (d) 72
12. 12.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 159 (c) 150 (d) 168
13. 13.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 303 (c) 280 (d) 313
14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 19 (b) 7 (c) 18 (d) 17
15. 15.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) 18 (b) 6 (c) 54 (d) 21
16. 16.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 525 (b) 516 (c) 422 (d) 526
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) 21 (c) 7 (d) 63
18. 18.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) 90 (b) 10 (c) 33 (d) 30
19. 19.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
20. 20.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) 63 (c) 180 (d) 20
21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 87? (a) 9 (b) 8 (c) 7 (d) 6
22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 3 (b) 2 (c) 4 (d) 5
23. 23.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 225 (c) 235 (d) 234
24. 24.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
25. 25.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 3 (b) 5 (c) 4 (d) 6
27. 27.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 315 (c) 324 (d) 288
28. 28.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) 72 (b) 24 (c) 27 (d) 8
29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 7 (b) 19 (c) 17 (d) 18
30. 30.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 484 (c) 609 (d) 619
31. 31.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 33 (c) 24 (d) 42
32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 4 (b) 12 (c) 10 (d) 11
33. 33.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) 36 (b) 11 (c) 99 (d) 33
34. 34.The numbers 14 to 22 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) 162 (c) 54 (d) 18
35. 35.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 86? (a) 8 (b) 13 (c) 16 (d) 15
37. 37.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 246 (c) 262 (d) 261
38. 38.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 244 (b) 258 (c) 249 (d) 259
39. 39.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 254 (b) 273 (c) 264 (d) 274
40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 4 (b) 16 (c) 14 (d) 15

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