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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 972 · 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 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
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 16 (d) 15
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 19 (b) 20 (c) 9 (d) 21
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 21 (b) 9 (c) 19 (d) 20
  5. 5.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
  6. 6.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) 153 (b) 17 (c) 54 (d) 51
  7. 7.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) 33 (b) 36 (c) 11 (d) 99
  8. 8.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 520 (b) 418 (c) 519 (d) 510
  9. 9.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
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  11. 11.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 156 (c) 166 (d) 165
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 7 (b) 18 (c) 19 (d) 17
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 5 (b) 2 (c) 3 (d) 4
  15. 15.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) 66 (d) 198
  16. 16.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 162 (c) 161 (d) 170
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 19 (d) 17
  18. 18.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 100 (c) 99 (d) 90
  19. 19.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 484 (c) 619 (d) 609
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  21. 21.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) 30 (b) 90 (c) 10 (d) 33
  22. 22.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 1 (b) 4 (c) 2 (d) 3
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 20 (b) 19 (c) 18 (d) 8
  24. 24.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 394 (c) 334 (d) 393
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 18 (b) 8 (c) 20 (d) 19
  26. 26.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  27. 27.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
  28. 28.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) 126 (b) 42 (c) 45 (d) 14
  29. 29.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) 48 (b) 135 (c) 45 (d) 15
  30. 30.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 595 (b) 594 (c) 585 (d) 468
  31. 31.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 80 (c) 89 (d) 98
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 17 (b) 18 (c) 7 (d) 19
  33. 33.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) 72 (d) 24
  34. 34.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) 207 (b) 69 (c) 72 (d) 23
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 3 (b) 4 (c) 2 (d) 5
  37. 37.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  38. 38.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 7 (d) 10
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 4 (b) 7 (c) 5 (d) 6
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 14 (b) 3 (c) 15 (d) 13

Answer key

  1. 18
  2. 15
  3. 20
  4. 20
  5. 27
  6. 51
  7. 33
  8. 519
  9. 109
  10. 6
  11. 165
  12. 5
  13. 18
  14. 4
  15. 66
  16. 161
  17. 18
  18. 99
  19. 618
  20. 7
  21. 30
  22. 3
  23. 19
  24. 393
  25. 19
  26. 6
  27. 57
  28. 42
  29. 45
  30. 594
  31. 89
  32. 18
  33. 72
  34. 69
  35. 4
  36. 4
  37. 4
  38. 8
  39. 6
  40. 14

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