Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 375 · 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 times is the digit 1 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 15 (d) 16
2. 2.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) 48 (b) 135 (c) 15 (d) 45
3. 3.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 420 (c) 513 (d) 523
4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 3 (b) 2 (c) 4 (d) 5
5. 5.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
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) 72 (b) 8 (c) 24 (d) 27
7. 7.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 274 (c) 303 (d) 294
8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 19 (b) 8 (c) 20 (d) 18
9. 9.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
10. 10.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 616 (c) 482 (d) 615
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) 5 (b) 18 (c) 15 (d) 45
12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 5 (d) 16
13. 13.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
14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 65? (a) 13 (b) 12 (c) 6 (d) 10
15. 15.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) 13 (b) 42 (c) 117 (d) 39
16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 5 (b) 16 (c) 17 (d) 15
17. 17.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 100 (c) 110 (d) 118
18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 4 (b) 3 (c) 5 (d) 6
19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 17 (b) 7 (c) 18 (d) 19
20. 20.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 372 (b) 441 (c) 451 (d) 450
21. 21.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) 153 (b) 17 (c) 51 (d) 54
22. 22.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
23. 23.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) 27 (b) 9 (c) 81 (d) 30
24. 24.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
25. 25.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 18 (d) 7
27. 27.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 190 (c) 180 (d) 189
28. 28.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 174 (c) 183 (d) 184
29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 30? (a) 14 (b) 3 (c) 13 (d) 12
30. 30.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) 11 (d) 36
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) 24 (b) 75 (c) 72 (d) 216
32. 32.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
33. 33.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) 51 (b) 48 (c) 16 (d) 144
34. 34.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 98 (c) 80 (d) 90
35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 71? (a) 16 (b) 18 (c) 7 (d) 17
36. 36.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) 20 (b) 60 (c) 63 (d) 180
37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 4 (b) 6 (c) 5 (d) 7
38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 16 (b) 4 (c) 14 (d) 15
39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 19 (b) 18 (c) 8 (d) 20
40. 40.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 114 (c) 105 (d) 96

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