Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 509 · 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 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 195 (b) 202 (c) 196 (d) 186
2. 2.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 304 (c) 303 (d) 274
3. 3.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 241 (d) 240
4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 1 (d) 2
5. 5.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 92 (c) 91 (d) 100
6. 6.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
7. 7.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 5 (d) 4
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) 8 (c) 27 (d) 72
9. 9.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 104 (c) 95 (d) 86
10. 10.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) 24 (b) 216 (c) 75 (d) 72
11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 16 (d) 17
12. 12.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) 21 (b) 24 (c) 7 (d) 63
13. 13.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 17 (b) 16 (c) 5 (d) 15
15. 15.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) 54 (b) 57 (c) 162 (d) 18
16. 16.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 5 (d) 7
17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 2 (d) 5
18. 18.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
19. 19.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 472 (c) 471 (d) 462
20. 20.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 15 (d) 14
22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 20 (b) 19 (c) 8 (d) 18
23. 23.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 573 (c) 454 (d) 574
24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 17 (b) 19 (c) 18 (d) 8
25. 25.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) 42 (b) 45 (c) 14 (d) 126
26. 26.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
27. 27.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 225 (d) 216
28. 28.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 5 (d) 14
30. 30.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 74 (c) 84 (d) 83
31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 6 (b) 3 (c) 4 (d) 5
32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 4 (b) 2 (c) 3 (d) 1
33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 2 (b) 3 (c) 5 (d) 4
34. 34.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 47 (c) 48 (d) 56
35. 35.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) 63 (b) 20 (c) 60 (d) 180
36. 36.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) 33 (d) 90
37. 37.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 375 (c) 376 (d) 322
38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 3 (b) 14 (c) 13 (d) 15
39. 39.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) 21 (c) 18 (d) 54
40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 2 (b) 1 (c) 4 (d) 3

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