Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 64 · 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 7 written when you write all the numbers from 1 to 60? (a) 6 (b) 7 (c) 5 (d) 4
2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 4 (b) 1 (c) 2 (d) 3
3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 18 (b) 19 (c) 20 (d) 8
4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 17 (b) 15 (c) 6 (d) 16
5. 5.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 396 (c) 487 (d) 486
6. 6.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) 117 (b) 42 (c) 13 (d) 39
7. 7.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
8. 8.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) 45 (b) 42 (c) 126 (d) 14
9. 9.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
10. 10.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) 24 (c) 72 (d) 75
11. 11.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 143 (b) 152 (c) 144 (d) 134
12. 12.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 427 (c) 417 (d) 356
13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 9 (d) 19
14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 18 (b) 7 (c) 17 (d) 19
15. 15.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
16. 16.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) 9 (b) 30 (c) 27 (d) 81
17. 17.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) 54 (c) 162 (d) 57
18. 18.A book has 105 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 198 (c) 210 (d) 208
19. 19.The numbers 16 to 24 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) 180 (c) 20 (d) 63
20. 20.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 384 (c) 468 (d) 469
21. 21.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 559 (c) 444 (d) 549
22. 22.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 368 (b) 444 (c) 435 (d) 445
23. 23.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 3 (d) 2
24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 8 (b) 19 (c) 18 (d) 20
25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 4 (b) 14 (c) 15 (d) 16
26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 20 (d) 9
27. 27.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 526 (b) 422 (c) 525 (d) 516
28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 19 (d) 18
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) 39 (b) 36 (c) 108 (d) 12
30. 30.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) 121 (c) 122 (d) 112
31. 31.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 224 (c) 229 (d) 228
32. 32.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) 23 (b) 69 (c) 207 (d) 72
33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 7 (d) 19
34. 34.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 2 (d) 1
35. 35.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 432 (c) 442 (d) 441
36. 36.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 63 (b) 54 (c) 64 (d) 72
37. 37.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 246 (c) 252 (d) 261
38. 38.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 576 (c) 586 (d) 462
39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 7 (d) 18
40. 40.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 92 (c) 74 (d) 83

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