Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 947 · 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 13? (a) 5 (b) 14 (c) 7 (d) 6
2. 2.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 175 (c) 184 (d) 176
3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 61? (a) 8 (b) 7 (c) 9 (d) 6
4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 21 (d) 20
5. 5.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 80 (c) 72 (d) 71
6. 6.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) 8 (b) 72 (c) 27 (d) 24
7. 7.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) 21 (b) 66 (c) 63 (d) 189
8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 72? (a) 7 (b) 18 (c) 19 (d) 17
9. 9.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) 69 (d) 66
10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 3 (b) 7 (c) 4 (d) 6
11. 11.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) 7 (b) 63 (c) 24 (d) 21
12. 12.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 190 (c) 172 (d) 181
13. 13.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) 54 (c) 18 (d) 6
14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 17 (b) 16 (c) 6 (d) 18
15. 15.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
16. 16.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 56 (c) 47 (d) 38
17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 60? (a) 4 (b) 6 (c) 7 (d) 5
18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 14 (b) 15 (c) 16 (d) 4
19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 14 (c) 15 (d) 16
20. 20.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 405 (c) 348 (d) 415
21. 21.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
22. 22.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 13 (d) 6
23. 23.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 294 (c) 304 (d) 274
24. 24.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 78 (c) 86 (d) 77
25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 6 (b) 7 (c) 8 (d) 5
26. 26.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) 261 (c) 262 (d) 246
27. 27.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) 162 (b) 18 (c) 54 (d) 57
28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 18 (b) 17 (c) 6 (d) 16
29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 16 (d) 5
30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 3 (b) 5 (c) 6 (d) 4
31. 31.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 78 (c) 96 (d) 87
32. 32.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 116 (c) 108 (d) 107
33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 4 (b) 3 (c) 2 (d) 5
34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 16 (b) 4 (c) 14 (d) 15
35. 35.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) 27 (c) 9 (d) 81
36. 36.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 164 (c) 173 (d) 174
37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 4 (b) 3 (c) 2 (d) 1
38. 38.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 258 (c) 268 (d) 267
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) 5 (c) 15 (d) 45
40. 40.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 5 (d) 16

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