Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 30 · 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 3 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 20 (d) 18
2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 7 (d) 5
3. 3.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) 42 (c) 14 (d) 45
4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 77? (a) 7 (b) 17 (c) 18 (d) 19
5. 5.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) 10 (b) 33 (c) 90 (d) 30
6. 6.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 9 (b) 18 (c) 19 (d) 20
8. 8.A book has 162 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 369 (b) 379 (c) 378 (d) 324
9. 9.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 631 (b) 492 (c) 621 (d) 630
10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 16 (b) 17 (c) 7 (d) 18
11. 11.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
12. 12.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 51 (c) 52 (d) 42
13. 13.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 122 (c) 113 (d) 114
14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 6 (b) 5 (c) 3 (d) 4
15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 17 (b) 9 (c) 18 (d) 15
16. 16.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 148 (c) 157 (d) 166
17. 17.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 421 (c) 411 (d) 352
18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 17 (b) 6 (c) 15 (d) 16
19. 19.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 2 (b) 4 (c) 5 (d) 3
21. 21.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) 144 (c) 48 (d) 16
22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 3 (d) 2
23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 6 (b) 7 (c) 5 (d) 4
24. 24.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 409 (b) 399 (c) 408 (d) 344
25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 3 (d) 2
26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 7 (b) 14 (c) 15 (d) 12
27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 19 (d) 18
28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 16 (b) 5 (c) 17 (d) 15
29. 29.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) 39 (c) 36 (d) 12
30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 7 (b) 4 (c) 5 (d) 6
31. 31.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 92 (c) 102 (d) 101
32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 15 (b) 6 (c) 16 (d) 17
33. 33.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) 284 (c) 319 (d) 309
34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 19 (b) 18 (c) 20 (d) 9
35. 35.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
36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 40? (a) 5 (b) 2 (c) 3 (d) 4
37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 16 (b) 4 (c) 15 (d) 14
38. 38.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) 18 (b) 6 (c) 21 (d) 54
39. 39.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) 17 (b) 51 (c) 153 (d) 54
40. 40.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) 327 (c) 336 (d) 337

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