Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 936 · 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.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) 69 (b) 207 (c) 23 (d) 72
2. 2.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) 27 (c) 24 (d) 8
3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 82? (a) 8 (b) 18 (c) 19 (d) 17
4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 15 (b) 4 (c) 14 (d) 13
5. 5.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 11 (b) 3 (c) 13 (d) 12
6. 6.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 483 (c) 394 (d) 474
7. 7.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 58 (c) 66 (d) 57
8. 8.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
9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 3 (d) 2
10. 10.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
11. 11.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) 45 (d) 15
12. 12.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
13. 13.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) 144 (b) 16 (c) 48 (d) 51
14. 14.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 94 (c) 93 (d) 84
15. 15.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 400 (c) 338 (d) 390
16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 15 (b) 3 (c) 14 (d) 13
17. 17.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 71? (a) 8 (b) 10 (c) 9 (d) 7
19. 19.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) 33 (c) 10 (d) 90
20. 20.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) 60 (b) 57 (c) 171 (d) 19
21. 21.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 12 (d) 9
22. 22.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
23. 23.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 421 (b) 352 (c) 411 (d) 420
24. 24.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
25. 25.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
26. 26.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) 126 (b) 45 (c) 14 (d) 42
27. 27.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 161 (c) 170 (d) 162
28. 28.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 58 (c) 50 (d) 49
29. 29.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
30. 30.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 125 (c) 134 (d) 126
31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 13 (b) 14 (c) 15 (d) 3
32. 32.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
33. 33.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) 180 (c) 63 (d) 20
34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 5 (b) 2 (c) 4 (d) 3
35. 35.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 469 (b) 384 (c) 459 (d) 468
36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 79? (a) 9 (b) 7 (c) 8 (d) 6
37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 66? (a) 18 (b) 16 (c) 17 (d) 6
38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 3 (b) 6 (c) 4 (d) 5
39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 20 (d) 21
40. 40.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 613 (c) 603 (d) 612

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