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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 186 · 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.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 14 (b) 4 (c) 13 (d) 15
  2. 2.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) 435 (c) 362 (d) 426
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 5 (b) 15 (c) 17 (d) 16
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 15 (b) 14 (c) 3 (d) 13
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 9 (d) 20
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 39? (a) 13 (b) 3 (c) 15 (d) 14
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 55? (a) 4 (b) 3 (c) 5 (d) 6
  9. 9.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) 54 (b) 18 (c) 162 (d) 57
  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) 75 (b) 72 (c) 24 (d) 216
  11. 11.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 105 (c) 96 (d) 114
  12. 12.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 3 (b) 9 (c) 8 (d) 10
  14. 14.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 580 (b) 570 (c) 579 (d) 458
  15. 15.The numbers 17 to 25 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) 189 (c) 21 (d) 63
  16. 16.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) 12 (b) 36 (c) 39 (d) 108
  17. 17.How many times is the digit 2 written when you write all the numbers from 1 to 57? (a) 16 (b) 15 (c) 17 (d) 5
  18. 18.How many times is the digit 7 written when you write all the numbers from 1 to 86? (a) 17 (b) 8 (c) 19 (d) 18
  19. 19.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) 135 (b) 45 (c) 48 (d) 15
  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) 66 (b) 198 (c) 22 (d) 69
  21. 21.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 6 (b) 5 (c) 4 (d) 3
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 15 (b) 16 (c) 17 (d) 6
  23. 23.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) 24 (b) 72 (c) 8 (d) 27
  24. 24.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  25. 25.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 17 (d) 18
  27. 27.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  28. 28.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 474 (b) 394 (c) 484 (d) 483
  29. 29.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 167 (b) 176 (c) 158 (d) 168
  30. 30.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) 180 (b) 60 (c) 20 (d) 63
  31. 31.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) 17 (c) 153 (d) 51
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  33. 33.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 292 (c) 331 (d) 330
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 18 (d) 20
  35. 35.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 56 (c) 47 (d) 38
  36. 36.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 519 (c) 529 (d) 528
  37. 37.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 18 (d) 20
  39. 39.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) 450 (c) 459 (d) 460
  40. 40.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) 42 (b) 13 (c) 39 (d) 117

Answer key

  1. 14
  2. 435
  3. 16
  4. 14
  5. 20
  6. 7
  7. 14
  8. 5
  9. 54
  10. 72
  11. 105
  12. 8
  13. 9
  14. 579
  15. 63
  16. 36
  17. 16
  18. 18
  19. 45
  20. 66
  21. 5
  22. 16
  23. 24
  24. 5
  25. 9
  26. 18
  27. 3
  28. 483
  29. 167
  30. 60
  31. 51
  32. 9
  33. 330
  34. 19
  35. 47
  36. 528
  37. 8
  38. 19
  39. 459
  40. 39

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