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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 568 · 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 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) 45 (b) 48 (c) 15 (d) 135
  2. 2.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 73 (c) 64 (d) 82
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 8 (b) 6 (c) 5 (d) 7
  4. 4.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) 39 (c) 13 (d) 117
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 20 (d) 8
  6. 6.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 59 (c) 60 (d) 68
  7. 7.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) 21 (c) 63 (d) 189
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 18 (d) 7
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 15 (b) 14 (c) 4 (d) 13
  10. 10.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 274 (c) 304 (d) 303
  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) 165 (b) 156 (c) 174 (d) 166
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  13. 13.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 136 (c) 154 (d) 145
  14. 14.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 585 (c) 586 (d) 462
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 53? (a) 4 (b) 5 (c) 3 (d) 6
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  17. 17.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 478 (c) 468 (d) 477
  18. 18.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 53 (c) 44 (d) 54
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 94? (a) 18 (b) 9 (c) 19 (d) 20
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 7 (d) 18
  21. 21.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) 27 (b) 72 (c) 24 (d) 8
  22. 22.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) 144 (b) 16 (c) 48 (d) 51
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 2 (b) 3 (c) 1 (d) 4
  24. 24.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
  25. 25.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) 162 (b) 18 (c) 57 (d) 54
  26. 26.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) 153 (c) 51 (d) 17
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 9 (b) 20 (c) 18 (d) 19
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 15 (b) 16 (c) 5 (d) 17
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 17 (b) 19 (c) 7 (d) 18
  30. 30.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) 74 (c) 92 (d) 83
  31. 31.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 591 (c) 601 (d) 600
  32. 32.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 3 (d) 1
  34. 34.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 21 (d) 20
  35. 35.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) 69 (c) 78 (d) 60
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 2 (b) 4 (c) 3 (d) 5
  37. 37.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) 20 (c) 180 (d) 63
  38. 38.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
  39. 39.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 152 (c) 134 (d) 143
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 8 (b) 20 (c) 18 (d) 19

Answer key

  1. 45
  2. 73
  3. 7
  4. 39
  5. 19
  6. 59
  7. 63
  8. 18
  9. 14
  10. 303
  11. 165
  12. 2
  13. 145
  14. 585
  15. 5
  16. 7
  17. 477
  18. 53
  19. 19
  20. 18
  21. 24
  22. 48
  23. 3
  24. 36
  25. 54
  26. 51
  27. 19
  28. 16
  29. 18
  30. 83
  31. 600
  32. 3
  33. 3
  34. 20
  35. 69
  36. 4
  37. 60
  38. 57
  39. 143
  40. 19

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