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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 576 · 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 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) 21 (b) 24 (c) 7 (d) 63
  2. 2.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) 90 (b) 30 (c) 33 (d) 10
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 4 (d) 5
  4. 4.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 104 (b) 114 (c) 113 (d) 122
  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) 9 (b) 30 (c) 27 (d) 81
  6. 6.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 208 (b) 195 (c) 204 (d) 205
  7. 7.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) 20 (b) 60 (c) 63 (d) 180
  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) 153 (d) 54
  9. 9.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 292 (c) 266 (d) 291
  10. 10.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
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 8 (b) 7 (c) 5 (d) 6
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 62? (a) 17 (b) 16 (c) 18 (d) 6
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 8 (d) 19
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 20 (b) 19 (c) 21 (d) 9
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 9 (d) 20
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  17. 17.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) 6 (b) 21 (c) 18 (d) 54
  18. 18.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  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) 8 (b) 27 (c) 24 (d) 72
  22. 22.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
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 17 (b) 7 (c) 16 (d) 18
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 3 (b) 14 (c) 13 (d) 15
  25. 25.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  26. 26.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) 176 (c) 166 (d) 175
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 18 (b) 19 (c) 9 (d) 20
  28. 28.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 87 (b) 88 (c) 78 (d) 96
  29. 29.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) 72 (b) 69 (c) 23 (d) 207
  30. 30.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) 170 (c) 162 (d) 161
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 4 (b) 3 (c) 2 (d) 5
  32. 32.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 600 (c) 478 (d) 610
  33. 33.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
  34. 34.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 18 (c) 5 (d) 45
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 64? (a) 18 (b) 17 (c) 16 (d) 6
  36. 36.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) 39 (c) 36 (d) 108
  37. 37.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 546 (b) 556 (c) 442 (d) 555
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 18 (d) 20
  39. 39.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 342 (c) 405 (d) 396
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 4 (d) 1

Answer key

  1. 21
  2. 30
  3. 6
  4. 113
  5. 27
  6. 204
  7. 60
  8. 51
  9. 291
  10. 54
  11. 7
  12. 17
  13. 19
  14. 20
  15. 20
  16. 6
  17. 18
  18. 3
  19. 2
  20. 7
  21. 24
  22. 66
  23. 17
  24. 14
  25. 5
  26. 175
  27. 19
  28. 87
  29. 69
  30. 161
  31. 4
  32. 609
  33. 45
  34. 15
  35. 17
  36. 36
  37. 555
  38. 19
  39. 405
  40. 3

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