Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 538 · 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 two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 4 (d) 3
2. 2.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10
3. 3.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 259 (b) 258 (c) 244 (d) 249
4. 4.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
5. 5.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 570 (c) 458 (d) 580
6. 6.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 13 (c) 7 (d) 6
7. 7.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) 168 (c) 150 (d) 160
8. 8.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 9 (b) 7 (c) 8 (d) 6
10. 10.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) 63 (b) 189 (c) 66 (d) 21
11. 11.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 181 (b) 172 (c) 190 (d) 182
12. 12.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) 51 (c) 153 (d) 17
13. 13.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 19 (d) 17
15. 15.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 70 (c) 69 (d) 60
16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 15 (b) 4 (c) 14 (d) 16
17. 17.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) 27 (c) 72 (d) 8
18. 18.A book has 151 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 302 (b) 346 (c) 345 (d) 336
19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 8 (b) 18 (c) 19 (d) 20
20. 20.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) 30 (b) 9 (c) 27 (d) 81
21. 21.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
22. 22.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) 126 (c) 14 (d) 45
23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 15 (b) 4 (c) 16 (d) 14
24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 8 (b) 11 (c) 12 (d) 9
25. 25.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) 21 (b) 6 (c) 18 (d) 54
26. 26.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 3 (b) 4 (c) 1 (d) 2
27. 27.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
28. 28.A book has 150 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 343 (c) 300 (d) 333
29. 29.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 417 (b) 426 (c) 356 (d) 427
30. 30.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) 180 (c) 60 (d) 20
31. 31.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) 10 (b) 33 (c) 30 (d) 90
32. 32.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 595 (c) 594 (d) 468
33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 17 (b) 14 (c) 9 (d) 16
34. 34.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) 216 (c) 24 (d) 72
35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 5 (b) 4 (c) 3 (d) 2
36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 16 (b) 6 (c) 17 (d) 18
37. 37.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 156 (c) 148 (d) 147
38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 19 (b) 18 (c) 7 (d) 17
39. 39.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 162 (c) 171 (d) 180
40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 9 (b) 6 (c) 7 (d) 8

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