Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 27 · 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 two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8
2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 21 (b) 9 (c) 19 (d) 20
3. 3.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 88 (c) 98 (d) 97
4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 20 (b) 9 (c) 21 (d) 19
5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 4 (b) 6 (c) 5 (d) 3
6. 6.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
7. 7.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) 171 (b) 57 (c) 19 (d) 60
8. 8.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
9. 9.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) 36 (b) 108 (c) 39 (d) 12
10. 10.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 152 (c) 144 (d) 143
11. 11.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) 63 (c) 66 (d) 21
12. 12.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 488 (b) 615 (c) 625 (d) 624
13. 13.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 360 (b) 312 (c) 361 (d) 351
14. 14.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) 8 (d) 24
15. 15.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 55 (c) 46 (d) 56
16. 16.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 434 (b) 544 (c) 534 (d) 543
17. 17.The numbers 3 to 11 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 7 (b) 21 (c) 24 (d) 63
18. 18.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 122 (c) 121 (d) 112
19. 19.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 243 (c) 244 (d) 351
20. 20.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 47 (b) 48 (c) 56 (d) 38
21. 21.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 45 (b) 54 (c) 46 (d) 36
22. 22.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 78 (c) 60 (d) 70
23. 23.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) 162 (c) 54 (d) 57
24. 24.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) 54 (b) 6 (c) 21 (d) 18
25. 25.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 70 (c) 61 (d) 52
26. 26.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
27. 27.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 28 (c) 46 (d) 38
28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 20 (d) 18
29. 29.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) 15 (b) 45 (c) 5 (d) 18
30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 14 (d) 15
31. 31.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
32. 32.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 4 (d) 2
33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 20 (b) 9 (c) 18 (d) 19
34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 84? (a) 17 (b) 19 (c) 8 (d) 18
35. 35.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
36. 36.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 22 (b) 198 (c) 69 (d) 66
37. 37.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 16 (d) 4
38. 38.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) 42 (c) 51 (d) 52
39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 4 (b) 6 (c) 3 (d) 5
40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 40? (a) 15 (b) 4 (c) 14 (d) 13

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