Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 934 · 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 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) 7 (c) 63 (d) 21
2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 6 (b) 5 (c) 4 (d) 7
3. 3.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) 21 (b) 54 (c) 18 (d) 6
4. 4.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 172 (c) 181 (d) 190
5. 5.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
6. 6.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 10 (d) 3
7. 7.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
8. 8.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
9. 9.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 464 (b) 579 (c) 589 (d) 588
10. 10.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 552 (c) 446 (d) 561
11. 11.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
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) 81 (b) 9 (c) 27 (d) 30
13. 13.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) 15 (b) 48 (c) 45 (d) 135
14. 14.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
15. 15.How many times is the digit 2 written when you write all the numbers from 1 to 59? (a) 17 (b) 15 (c) 5 (d) 16
16. 16.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 11 (c) 36 (d) 33
17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 6 (b) 5 (c) 7 (d) 8
18. 18.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
19. 19.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 336 (c) 397 (d) 387
20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 51? (a) 15 (b) 5 (c) 16 (d) 14
21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 14 (b) 16 (c) 15 (d) 4
22. 22.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 520 (c) 418 (d) 510
23. 23.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 207 (c) 208 (d) 210
24. 24.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 571 (b) 561 (c) 452 (d) 570
25. 25.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 1 (d) 2
27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 4 (b) 7 (c) 5 (d) 6
28. 28.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) 51 (b) 17 (c) 153 (d) 54
29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 5 (b) 7 (c) 4 (d) 6
30. 30.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 142 (c) 150 (d) 141
31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 65? (a) 17 (b) 6 (c) 18 (d) 16
32. 32.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 366 (c) 357 (d) 316
33. 33.A book has 217 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 534 (b) 543 (c) 544 (d) 434
34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 2 (b) 5 (c) 3 (d) 4
35. 35.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 529 (b) 424 (c) 528 (d) 519
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) 88 (b) 70 (c) 79 (d) 80
37. 37.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 86 (c) 95 (d) 96
38. 38.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
39. 39.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
40. 40.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

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