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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 333 · 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 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) 54 (b) 21 (c) 6 (d) 18
  2. 2.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 190 (b) 189 (c) 180 (d) 198
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 18 (d) 19
  6. 6.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 565 (b) 448 (c) 555 (d) 564
  7. 7.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) 11 (b) 99 (c) 36 (d) 33
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 8 (b) 18 (c) 19 (d) 17
  9. 9.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 34 (c) 33 (d) 24
  10. 10.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 292 (b) 282 (c) 291 (d) 266
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 17 (b) 16 (c) 5 (d) 15
  12. 12.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) 51 (b) 16 (c) 48 (d) 144
  13. 13.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 41 (b) 42 (c) 50 (d) 32
  14. 14.The numbers 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 216 (b) 75 (c) 72 (d) 24
  15. 15.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 160 (c) 152 (d) 151
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 15 (b) 3 (c) 14 (d) 13
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 1 (d) 2
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 16 (b) 5 (c) 17 (d) 15
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 8 (b) 6 (c) 7 (d) 5
  21. 21.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 7 (b) 4 (c) 5 (d) 6
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 15 (b) 18 (c) 17 (d) 9
  24. 24.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 12 (b) 4 (c) 10 (d) 11
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 6 (b) 7 (c) 5 (d) 4
  27. 27.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 186 (d) 177
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 7 (b) 9 (c) 8 (d) 6
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 6 (b) 8 (c) 7 (d) 9
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 95? (a) 21 (b) 9 (c) 20 (d) 19
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 16 (d) 7
  32. 32.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) 10 (b) 90 (c) 33 (d) 30
  33. 33.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 219 (b) 228 (c) 224 (d) 229
  34. 34.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 50 (c) 68 (d) 59
  35. 35.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) 66 (b) 69 (c) 22 (d) 198
  36. 36.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 362 (c) 436 (d) 435
  37. 37.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) 162 (b) 18 (c) 57 (d) 54
  38. 38.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
  39. 39.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 155 (b) 164 (c) 146 (d) 156
  40. 40.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 140 (c) 148 (d) 139

Answer key

  1. 18
  2. 189
  3. 5
  4. 7
  5. 19
  6. 564
  7. 33
  8. 18
  9. 33
  10. 291
  11. 16
  12. 48
  13. 41
  14. 72
  15. 151
  16. 4
  17. 14
  18. 3
  19. 16
  20. 7
  21. 6
  22. 6
  23. 17
  24. 9
  25. 11
  26. 6
  27. 177
  28. 8
  29. 8
  30. 20
  31. 17
  32. 30
  33. 228
  34. 59
  35. 66
  36. 435
  37. 54
  38. 135
  39. 155
  40. 139

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