Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 741 · 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) 54 (b) 153 (c) 17 (d) 51
2. 2.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 502 (c) 406 (d) 501
3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 17 (b) 16 (c) 18 (d) 6
4. 4.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) 162 (b) 57 (c) 18 (d) 54
5. 5.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) 126 (c) 45 (d) 42
6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 4 (b) 15 (c) 16 (d) 14
7. 7.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
8. 8.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 458 (c) 579 (d) 580
9. 9.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) 66 (b) 69 (c) 22 (d) 198
10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 15 (d) 14
11. 11.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 630 (b) 492 (c) 621 (d) 631
12. 12.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 627 (c) 628 (d) 618
13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 17 (d) 16
14. 14.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 17 (d) 8
15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 6 (b) 17 (c) 18 (d) 16
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) 45 (b) 15 (c) 48 (d) 135
17. 17.How many times is the digit 5 written when you write all the numbers from 1 to 60? (a) 16 (b) 17 (c) 6 (d) 15
18. 18.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
19. 19.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 456 (c) 465 (d) 382
20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 13 (c) 14 (d) 15
21. 21.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) 21 (b) 24 (c) 63 (d) 7
22. 22.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 523 (b) 522 (c) 513 (d) 420
23. 23.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
24. 24.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) 16 (c) 48 (d) 144
25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 18 (b) 17 (c) 19 (d) 8
26. 26.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
27. 27.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
28. 28.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) 24 (d) 8
29. 29.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 346 (c) 411 (d) 412
30. 30.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) 39 (b) 117 (c) 42 (d) 13
31. 31.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) 114 (c) 113 (d) 122
32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 5 (b) 14 (c) 16 (d) 15
33. 33.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) 576 (c) 456 (d) 577
34. 34.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 92 (c) 83 (d) 84
35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 4 (d) 5
36. 36.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 79 (c) 80 (d) 88
37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 6 (b) 7 (c) 4 (d) 5
38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 5 (b) 7 (c) 6 (d) 8
39. 39.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 150 (c) 140 (d) 158
40. 40.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) 6 (b) 54 (c) 21 (d) 18

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