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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 592 · 40 questions
TalentJR

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.

NameDateTime takenScore ___ / 40
  1. 1.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) 8 (c) 27 (d) 24
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 5 (b) 15 (c) 17 (d) 16
  3. 3.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) 24 (c) 21 (d) 63
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 13 (b) 14 (c) 3 (d) 12
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 19 (d) 9
  6. 6.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 259 (c) 258 (d) 244
  7. 7.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) 69 (b) 72 (c) 207 (d) 23
  8. 8.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 400 (c) 338 (d) 390
  9. 9.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) 54 (d) 153
  10. 10.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) 33 (b) 10 (c) 90 (d) 30
  11. 11.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) 75 (b) 216 (c) 24 (d) 72
  12. 12.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  13. 13.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 447 (c) 448 (d) 438
  14. 14.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) 60 (c) 57 (d) 19
  15. 15.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 81 (b) 90 (c) 72 (d) 82
  16. 16.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) 57 (b) 54 (c) 162 (d) 18
  17. 17.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) 12 (c) 36 (d) 108
  18. 18.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 101 (c) 92 (d) 102
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  20. 20.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) 69 (c) 198 (d) 66
  21. 21.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 76 (c) 86 (d) 85
  22. 22.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
  23. 23.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 630 (c) 631 (d) 621
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  25. 25.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 8 (d) 9
  26. 26.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) 126 (c) 42 (d) 14
  27. 27.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) 18 (c) 21 (d) 6
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 4 (b) 7 (c) 5 (d) 6
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 3 (b) 4 (c) 5 (d) 2
  31. 31.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 211 (c) 201 (d) 210
  32. 32.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  33. 33.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 8 (b) 7 (c) 9 (d) 6
  35. 35.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 362 (c) 426 (d) 435
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 3 (b) 4 (c) 5 (d) 6
  37. 37.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 498 (b) 410 (c) 507 (d) 508
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 1 (b) 3 (c) 2 (d) 4
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 15 (b) 5 (c) 16 (d) 17
  40. 40.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 109 (c) 118 (d) 110

Answer key

  1. 24
  2. 16
  3. 21
  4. 13
  5. 19
  6. 258
  7. 69
  8. 399
  9. 51
  10. 30
  11. 72
  12. 7
  13. 447
  14. 57
  15. 81
  16. 54
  17. 36
  18. 101
  19. 7
  20. 66
  21. 85
  22. 39
  23. 630
  24. 8
  25. 9
  26. 42
  27. 18
  28. 5
  29. 6
  30. 4
  31. 210
  32. 3
  33. 3
  34. 8
  35. 435
  36. 5
  37. 507
  38. 3
  39. 16
  40. 109

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