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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 506 · 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 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
  2. 2.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 129 (b) 138 (c) 120 (d) 130
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 17 (d) 6
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  5. 5.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 262 (c) 261 (d) 246
  6. 6.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 126 (c) 117 (d) 108
  7. 7.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 447 (c) 457 (d) 456
  8. 8.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 406 (b) 492 (c) 501 (d) 502
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 3 (b) 13 (c) 15 (d) 14
  10. 10.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 514 (b) 504 (c) 513 (d) 414
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 3 (b) 14 (c) 13 (d) 15
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 4 (d) 5
  13. 13.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 164 (c) 182 (d) 173
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 16 (b) 17 (c) 15 (d) 5
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 16 (b) 17 (c) 5 (d) 15
  16. 16.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 131 (b) 122 (c) 132 (d) 140
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 3 (b) 6 (c) 4 (d) 5
  18. 18.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 122 (c) 121 (d) 112
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 20 (b) 18 (c) 9 (d) 19
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 5 (b) 3 (c) 6 (d) 4
  21. 21.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) 180 (c) 63 (d) 20
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 89? (a) 18 (b) 20 (c) 8 (d) 19
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 18 (b) 8 (c) 19 (d) 20
  24. 24.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) 45 (b) 15 (c) 18 (d) 5
  25. 25.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 128 (c) 110 (d) 119
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 3 (b) 5 (c) 4 (d) 6
  27. 27.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  28. 28.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) 51 (d) 48
  29. 29.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 177 (b) 168 (c) 186 (d) 178
  30. 30.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) 117 (c) 39 (d) 13
  31. 31.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) 33 (b) 10 (c) 90 (d) 30
  32. 32.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) 18 (b) 54 (c) 6 (d) 21
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 60? (a) 7 (b) 5 (c) 6 (d) 4
  34. 34.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 49? (a) 3 (b) 4 (c) 6 (d) 5
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 6 (b) 5 (c) 4 (d) 7
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 61? (a) 6 (b) 16 (c) 17 (d) 15
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 4 (b) 7 (c) 6 (d) 5
  39. 39.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 229 (c) 224 (d) 219
  40. 40.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) 99 (b) 36 (c) 33 (d) 11

Answer key

  1. 54
  2. 129
  3. 17
  4. 2
  5. 261
  6. 117
  7. 456
  8. 501
  9. 14
  10. 513
  11. 14
  12. 4
  13. 173
  14. 16
  15. 16
  16. 131
  17. 5
  18. 121
  19. 19
  20. 5
  21. 60
  22. 19
  23. 19
  24. 15
  25. 119
  26. 5
  27. 6
  28. 48
  29. 177
  30. 39
  31. 30
  32. 18
  33. 6
  34. 9
  35. 5
  36. 6
  37. 16
  38. 6
  39. 228
  40. 33

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