Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 356 · 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 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) 99 (b) 33 (c) 36 (d) 11
2. 2.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) 72 (b) 23 (c) 69 (d) 207
3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 7 (b) 18 (c) 17 (d) 19
4. 4.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) 42 (b) 13 (c) 117 (d) 39
5. 5.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) 162 (d) 170
6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 19 (b) 21 (c) 9 (d) 20
7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 17 (b) 5 (c) 16 (d) 15
8. 8.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
9. 9.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 357 (c) 348 (d) 358
10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 58? (a) 17 (b) 5 (c) 16 (d) 15
11. 11.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) 18 (b) 54 (c) 57 (d) 162
12. 12.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 5 (d) 15
13. 13.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) 171 (c) 57 (d) 19
14. 14.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
15. 15.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
16. 16.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 6 (b) 8 (c) 5 (d) 7
18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 16 (b) 15 (c) 9 (d) 13
19. 19.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) 9 (b) 81 (c) 30 (d) 27
20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 6 (b) 5 (c) 7 (d) 8
21. 21.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 375 (c) 366 (d) 376
22. 22.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
23. 23.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 7 (d) 13
24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 15 (b) 16 (c) 5 (d) 17
25. 25.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) 48 (b) 16 (c) 51 (d) 144
26. 26.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) 45 (b) 5 (c) 18 (d) 15
27. 27.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 447 (c) 370 (d) 448
28. 28.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 20 (d) 18
29. 29.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) 45 (b) 126 (c) 14 (d) 42
30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 2 (b) 4 (c) 1 (d) 3
31. 31.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) 216 (b) 75 (c) 24 (d) 72
32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 7 (b) 4 (c) 6 (d) 5
33. 33.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) 107 (c) 108 (d) 116
34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 16 (b) 17 (c) 15 (d) 5
35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 18 (d) 17
36. 36.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5
37. 37.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 3 (b) 4 (c) 6 (d) 5
39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 7 (d) 16
40. 40.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 36 (c) 12 (d) 39

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