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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 816 · 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 9 written when you write all the numbers from 1 to 31? (a) 3 (b) 1 (c) 2 (d) 4
  2. 2.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 40 (c) 58 (d) 49
  3. 3.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 326 (b) 382 (c) 381 (d) 372
  4. 4.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) 13 (b) 39 (c) 42 (d) 117
  5. 5.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 178 (c) 170 (d) 169
  6. 6.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) 16 (b) 51 (c) 144 (d) 48
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 11 (d) 8
  8. 8.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) 18 (c) 5 (d) 15
  9. 9.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) 198 (b) 22 (c) 69 (d) 66
  10. 10.A book has 75 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 142 (c) 132 (d) 141
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 39? (a) 4 (b) 5 (c) 2 (d) 3
  12. 12.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 385 (b) 384 (c) 328 (d) 375
  13. 13.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) 81 (c) 27 (d) 30
  14. 14.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) 171 (b) 57 (c) 60 (d) 19
  15. 15.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  16. 16.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 50 (c) 41 (d) 42
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 18 (b) 8 (c) 19 (d) 20
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 18 (b) 20 (c) 19 (d) 8
  20. 20.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  21. 21.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 241 (b) 232 (c) 231 (d) 240
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 19 (b) 8 (c) 20 (d) 18
  23. 23.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 136 (c) 128 (d) 127
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 14 (b) 3 (c) 15 (d) 13
  25. 25.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 164 (c) 155 (d) 146
  26. 26.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) 11 (c) 33 (d) 36
  27. 27.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  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) 96 (b) 88 (c) 87 (d) 78
  29. 29.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 1 (d) 3
  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) 63 (b) 7 (c) 24 (d) 21
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 7 (b) 18 (c) 17 (d) 19
  32. 32.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 490 (c) 627 (d) 628
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 16 (d) 5
  34. 34.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) 57 (b) 18 (c) 162 (d) 54
  35. 35.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 22 (c) 40 (d) 31
  36. 36.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) 136 (c) 135 (d) 144
  37. 37.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 349 (c) 339 (d) 304
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 5 (b) 16 (c) 14 (d) 15
  39. 39.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 3 (b) 6 (c) 5 (d) 4

Answer key

  1. 3
  2. 49
  3. 381
  4. 39
  5. 169
  6. 48
  7. 9
  8. 15
  9. 66
  10. 141
  11. 4
  12. 384
  13. 27
  14. 57
  15. 6
  16. 41
  17. 19
  18. 5
  19. 19
  20. 8
  21. 240
  22. 19
  23. 127
  24. 14
  25. 155
  26. 33
  27. 5
  28. 87
  29. 3
  30. 21
  31. 18
  32. 627
  33. 16
  34. 54
  35. 31
  36. 135
  37. 348
  38. 15
  39. 4
  40. 5

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