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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 646 · 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) 144 (b) 48 (c) 16 (d) 51
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 4 (b) 14 (c) 13 (d) 15
  3. 3.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
  4. 4.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) 207 (c) 69 (d) 23
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 5 (b) 3 (c) 2 (d) 4
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 5 (b) 3 (c) 4 (d) 6
  7. 7.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 174 (c) 173 (d) 164
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 18 (b) 20 (c) 19 (d) 9
  9. 9.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 71 (b) 80 (c) 72 (d) 62
  10. 10.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 351 (b) 243 (c) 234 (d) 244
  11. 11.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 5 (d) 16
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 2 (d) 4
  14. 14.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 120 (c) 130 (d) 129
  15. 15.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 88 (c) 78 (d) 87
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  17. 17.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) 39 (b) 42 (c) 13 (d) 117
  18. 18.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 212 (b) 201 (c) 211 (d) 210
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 19 (b) 18 (c) 7 (d) 17
  20. 20.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) 14 (b) 42 (c) 126 (d) 45
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 4 (b) 6 (c) 7 (d) 5
  22. 22.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 85 (b) 76 (c) 86 (d) 94
  23. 23.A book has 131 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 276 (b) 286 (c) 285 (d) 262
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 6 (d) 7
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 16 (b) 15 (c) 17 (d) 6
  26. 26.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  27. 27.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 16 (c) 5 (d) 3
  28. 28.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 82 (c) 81 (d) 72
  29. 29.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) 5 (c) 18 (d) 45
  30. 30.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) 7 (b) 24 (c) 21 (d) 63
  31. 31.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) 189 (b) 21 (c) 66 (d) 63
  32. 32.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 64 (c) 74 (d) 73
  33. 33.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) 30 (b) 27 (c) 9 (d) 81
  34. 34.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 5 (d) 10
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 55? (a) 6 (b) 4 (c) 3 (d) 5
  36. 36.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 9 (d) 10
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  38. 38.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 4 (d) 5
  39. 39.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
  40. 40.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 406 (c) 502 (d) 501

Answer key

  1. 48
  2. 14
  3. 24
  4. 69
  5. 4
  6. 5
  7. 173
  8. 19
  9. 71
  10. 243
  11. 9
  12. 16
  13. 4
  14. 129
  15. 87
  16. 2
  17. 39
  18. 210
  19. 18
  20. 42
  21. 6
  22. 85
  23. 285
  24. 6
  25. 16
  26. 2
  27. 4
  28. 81
  29. 15
  30. 21
  31. 63
  32. 73
  33. 27
  34. 6
  35. 5
  36. 8
  37. 8
  38. 5
  39. 60
  40. 501

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