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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 395 · 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.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 4 (b) 6 (c) 5 (d) 3
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 20 (b) 9 (c) 21 (d) 19
  4. 4.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) 33 (b) 99 (c) 36 (d) 11
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 15 (b) 16 (c) 4 (d) 14
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 3 (b) 5 (c) 6 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  8. 8.A book has 55 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 92 (c) 102 (d) 101
  9. 9.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  10. 10.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 480 (c) 603 (d) 612
  11. 11.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) 19 (b) 171 (c) 57 (d) 60
  12. 12.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
  13. 13.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 261 (c) 252 (d) 262
  14. 14.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) 10 (d) 33
  15. 15.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 126 (c) 134 (d) 125
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 8 (b) 18 (c) 19 (d) 20
  17. 17.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) 23 (b) 72 (c) 69 (d) 207
  18. 18.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) 36 (b) 12 (c) 39 (d) 108
  19. 19.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 142 (c) 124 (d) 133
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 3 (b) 2 (c) 5 (d) 4
  21. 21.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 108 (c) 118 (d) 117
  22. 22.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 49 (b) 50 (c) 40 (d) 58
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 3 (b) 4 (c) 6 (d) 5
  24. 24.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 30 (c) 39 (d) 40
  25. 25.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) 66 (c) 48 (d) 57
  26. 26.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  27. 27.A book has 201 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 402 (c) 496 (d) 486
  28. 28.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) 54 (d) 153
  29. 29.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  30. 30.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 190 (c) 180 (d) 189
  31. 31.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 348 (c) 357 (d) 358
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 14 (b) 3 (c) 15 (d) 13
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 1 (d) 3
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 73? (a) 9 (b) 7 (c) 12 (d) 11
  35. 35.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) 21 (d) 6
  36. 36.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 98 (c) 97 (d) 88
  37. 37.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 4 (d) 6
  38. 38.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
  39. 39.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) 45 (b) 42 (c) 14 (d) 126
  40. 40.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

Answer key

  1. 5
  2. 9
  3. 20
  4. 33
  5. 15
  6. 5
  7. 7
  8. 101
  9. 8
  10. 612
  11. 57
  12. 45
  13. 261
  14. 30
  15. 125
  16. 19
  17. 69
  18. 36
  19. 133
  20. 4
  21. 117
  22. 49
  23. 5
  24. 39
  25. 57
  26. 3
  27. 495
  28. 51
  29. 2
  30. 189
  31. 357
  32. 14
  33. 3
  34. 11
  35. 18
  36. 97
  37. 5
  38. 17
  39. 42
  40. 71

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