Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 232 · 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 49? (a) 14 (b) 16 (c) 4 (d) 15
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) 45 (b) 135 (c) 15 (d) 48
3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 55? (a) 15 (b) 17 (c) 5 (d) 16
4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 18 (b) 20 (c) 8 (d) 19
5. 5.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) 19 (d) 171
6. 6.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) 162 (d) 57
7. 7.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 330 (c) 292 (d) 321
8. 8.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) 39 (c) 117 (d) 42
9. 9.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 4 (d) 10
10. 10.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 337 (c) 336 (d) 327
11. 11.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
12. 12.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
13. 13.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) 14 (b) 42 (c) 126 (d) 45
14. 14.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 318 (b) 319 (c) 284 (d) 309
15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 76? (a) 6 (b) 5 (c) 8 (d) 7
16. 16.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) 189 (b) 66 (c) 21 (d) 63
17. 17.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 141 (c) 132 (d) 142
18. 18.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 19 (b) 7 (c) 18 (d) 17
19. 19.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 631 (c) 630 (d) 621
20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 17 (d) 7
21. 21.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) 72 (d) 24
22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 20 (d) 9
23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 6 (b) 9 (c) 8 (d) 7
24. 24.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 4 (d) 2
25. 25.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) 15 (c) 45 (d) 5
26. 26.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 622 (b) 612 (c) 486 (d) 621
27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 9 (d) 21
28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 5 (b) 15 (c) 16 (d) 17
29. 29.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 28 (b) 37 (c) 38 (d) 46
30. 30.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 9 (b) 4 (c) 8 (d) 6
32. 32.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 471 (c) 386 (d) 462
33. 33.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) 27 (b) 72 (c) 8 (d) 24
34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 5 (b) 7 (c) 6 (d) 4
35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 13 (b) 15 (c) 3 (d) 14
36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 8 (b) 6 (c) 7 (d) 5
37. 37.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) 180 (c) 63 (d) 60
38. 38.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 567 (c) 568 (d) 558
39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 20 (b) 19 (c) 8 (d) 18
40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 64? (a) 17 (b) 18 (c) 6 (d) 16

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