Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 153 · 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 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
2. 2.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
3. 3.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 5 (b) 3 (c) 6 (d) 4
5. 5.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 440 (c) 543 (d) 553
6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 18 (b) 19 (c) 8 (d) 17
7. 7.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 474 (c) 483 (d) 394
8. 8.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) 30 (d) 81
9. 9.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 69 (c) 78 (d) 60
10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 33? (a) 2 (b) 3 (c) 1 (d) 4
11. 11.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) 19 (d) 57
12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 7 (b) 4 (c) 6 (d) 5
13. 13.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 589 (b) 464 (c) 588 (d) 579
14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 54? (a) 3 (b) 6 (c) 5 (d) 4
15. 15.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 332 (c) 391 (d) 390
16. 16.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) 15 (c) 45 (d) 135
17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 7 (b) 18 (c) 19 (d) 17
18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 9 (d) 18
19. 19.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 585 (c) 586 (d) 576
20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 89? (a) 19 (b) 20 (c) 8 (d) 18
21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 16 (b) 15 (c) 6 (d) 17
22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 17 (d) 7
23. 23.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
24. 24.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) 24 (b) 21 (c) 63 (d) 7
25. 25.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 136 (b) 135 (c) 126 (d) 144
26. 26.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 126 (c) 134 (d) 125
27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 19 (b) 17 (c) 7 (d) 18
28. 28.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 86 (c) 68 (d) 77
29. 29.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 577 (c) 576 (d) 456
30. 30.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 242 (c) 246 (d) 255
31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 8 (b) 18 (c) 20 (d) 19
32. 32.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) 45 (d) 15
33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 64? (a) 18 (b) 6 (c) 16 (d) 17
34. 34.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) 207 (c) 69 (d) 23
35. 35.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) 24 (b) 27 (c) 72 (d) 8
36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 58? (a) 5 (b) 6 (c) 3 (d) 4
37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 7 (d) 18
38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 18 (b) 16 (c) 7 (d) 17
39. 39.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) 117 (c) 39 (d) 42
40. 40.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 9 (d) 11

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