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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 292 · 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 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) 16 (b) 144 (c) 48 (d) 51
  2. 2.A book has 198 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 487 (b) 477 (c) 396 (d) 486
  3. 3.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) 75 (c) 24 (d) 72
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 20 (b) 19 (c) 8 (d) 18
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 11 (b) 10 (c) 12 (d) 4
  6. 6.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) 19 (b) 60 (c) 57 (d) 171
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 3 (b) 4 (c) 2 (d) 5
  8. 8.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
  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) 60 (c) 78 (d) 69
  10. 10.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 184 (b) 166 (c) 176 (d) 175
  11. 11.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 34? (a) 13 (b) 3 (c) 15 (d) 14
  13. 13.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 471 (c) 386 (d) 472
  14. 14.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 99 (c) 100 (d) 108
  15. 15.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  16. 16.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) 42 (b) 14 (c) 45 (d) 126
  17. 17.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  18. 18.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  19. 19.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 114 (c) 123 (d) 124
  20. 20.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) 162 (c) 18 (d) 54
  21. 21.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) 42 (d) 39
  22. 22.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 4 (b) 5 (c) 3 (d) 2
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 18 (b) 19 (c) 20 (d) 8
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 19 (b) 21 (c) 20 (d) 9
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 14 (b) 16 (c) 4 (d) 15
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 5 (b) 4 (c) 6 (d) 7
  28. 28.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 171 (c) 180 (d) 172
  29. 29.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 93 (b) 84 (c) 102 (d) 94
  30. 30.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 619 (b) 484 (c) 618 (d) 609
  31. 31.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  33. 33.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  34. 34.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 5 (b) 6 (c) 4 (d) 3
  36. 36.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) 30 (c) 9 (d) 27
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 18 (b) 7 (c) 17 (d) 16
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 53? (a) 4 (b) 6 (c) 3 (d) 5
  39. 39.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
  40. 40.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 459 (c) 450 (d) 460

Answer key

  1. 48
  2. 486
  3. 72
  4. 19
  5. 11
  6. 57
  7. 4
  8. 51
  9. 69
  10. 175
  11. 5
  12. 14
  13. 471
  14. 99
  15. 6
  16. 42
  17. 9
  18. 4
  19. 123
  20. 54
  21. 39
  22. 8
  23. 4
  24. 19
  25. 20
  26. 15
  27. 6
  28. 171
  29. 93
  30. 618
  31. 4
  32. 6
  33. 2
  34. 2
  35. 5
  36. 27
  37. 17
  38. 5
  39. 465
  40. 459

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