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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 703 · 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 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) 5 (b) 18 (c) 45 (d) 15
  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) 15 (d) 16
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 8 (b) 7 (c) 10 (d) 9
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 4 (d) 10
  5. 5.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 80 (c) 62 (d) 71
  6. 6.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 90 (c) 89 (d) 98
  7. 7.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) 108 (c) 39 (d) 36
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 19 (b) 8 (c) 20 (d) 18
  9. 9.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 238 (c) 249 (d) 250
  10. 10.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 123 (c) 114 (d) 132
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 8 (b) 19 (c) 20 (d) 18
  12. 12.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) 8 (d) 24
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 20 (b) 8 (c) 19 (d) 18
  14. 14.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  15. 15.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 144 (c) 135 (d) 136
  16. 16.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 358 (b) 348 (c) 310 (d) 357
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 94? (a) 19 (b) 21 (c) 9 (d) 20
  18. 18.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 418 (c) 350 (d) 417
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 18 (b) 9 (c) 19 (d) 20
  20. 20.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) 63 (b) 24 (c) 21 (d) 7
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 7 (b) 4 (c) 5 (d) 6
  22. 22.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 231 (c) 241 (d) 240
  23. 23.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) 10 (c) 33 (d) 30
  24. 24.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 414 (c) 514 (d) 504
  25. 25.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  26. 26.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 181 (c) 172 (d) 182
  27. 27.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 48 (c) 57 (d) 66
  28. 28.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) 6 (d) 18
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 2 (d) 3
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 5 (b) 15 (c) 16 (d) 17
  31. 31.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) 60 (b) 19 (c) 171 (d) 57
  32. 32.A book has 147 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 333 (b) 334 (c) 294 (d) 324
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 8 (b) 7 (c) 9 (d) 3
  34. 34.A book has 232 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 579 (b) 589 (c) 464 (d) 588
  35. 35.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 45 (b) 54 (c) 36 (d) 46
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 4 (d) 2
  37. 37.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 67 (b) 68 (c) 76 (d) 58
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 89? (a) 20 (b) 8 (c) 18 (d) 19
  39. 39.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 7 (d) 17
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 14 (b) 13 (c) 15 (d) 4

Answer key

  1. 15
  2. 15
  3. 9
  4. 3
  5. 71
  6. 89
  7. 36
  8. 19
  9. 249
  10. 123
  11. 19
  12. 24
  13. 19
  14. 4
  15. 135
  16. 357
  17. 20
  18. 417
  19. 19
  20. 21
  21. 6
  22. 240
  23. 30
  24. 513
  25. 9
  26. 181
  27. 57
  28. 18
  29. 3
  30. 16
  31. 57
  32. 333
  33. 8
  34. 588
  35. 45
  36. 4
  37. 67
  38. 19
  39. 18
  40. 14

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