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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 809 · 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.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 32 (c) 22 (d) 31
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 19 (b) 8 (c) 18 (d) 20
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 3 (b) 6 (c) 5 (d) 4
  4. 4.How many times is the digit 4 written when you write all the numbers from 1 to 60? (a) 6 (b) 17 (c) 16 (d) 15
  5. 5.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 82 (c) 74 (d) 73
  6. 6.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
  7. 7.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 80 (c) 89 (d) 98
  8. 8.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 123 (b) 124 (c) 114 (d) 132
  9. 9.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 552 (b) 446 (c) 562 (d) 561
  10. 10.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) 246 (c) 261 (d) 262
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 9 (b) 19 (c) 18 (d) 20
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 17 (b) 18 (c) 8 (d) 19
  13. 13.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 21 (b) 9 (c) 20 (d) 19
  14. 14.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 208 (c) 195 (d) 205
  15. 15.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) 48 (b) 144 (c) 51 (d) 16
  16. 16.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) 24 (b) 72 (c) 216 (d) 75
  17. 17.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 14 (c) 5 (d) 7
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 1 (d) 3
  19. 19.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) 39 (c) 108 (d) 12
  20. 20.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 142 (c) 151 (d) 152
  21. 21.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) 15 (d) 5
  22. 22.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 7 (d) 8
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 19 (d) 20
  24. 24.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 149 (b) 150 (c) 140 (d) 158
  25. 25.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 462 (c) 576 (d) 586
  26. 26.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  27. 27.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 3 (d) 2
  28. 28.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
  29. 29.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 342 (b) 406 (c) 396 (d) 405
  30. 30.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) 33 (d) 10
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 16 (b) 6 (c) 17 (d) 15
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 19 (d) 21
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 71? (a) 17 (b) 18 (c) 7 (d) 16
  34. 34.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 18 (d) 1
  35. 35.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 20 (b) 8 (c) 19 (d) 18
  37. 37.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 273 (b) 254 (c) 264 (d) 274
  38. 38.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 240 (c) 238 (d) 250
  39. 39.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) 18 (b) 162 (c) 57 (d) 54
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 6 (b) 4 (c) 7 (d) 5

Answer key

  1. 31
  2. 19
  3. 5
  4. 16
  5. 73
  6. 18
  7. 89
  8. 123
  9. 561
  10. 261
  11. 19
  12. 18
  13. 20
  14. 204
  15. 48
  16. 72
  17. 6
  18. 3
  19. 36
  20. 151
  21. 15
  22. 7
  23. 19
  24. 149
  25. 585
  26. 6
  27. 3
  28. 7
  29. 405
  30. 30
  31. 16
  32. 20
  33. 17
  34. 2
  35. 5
  36. 19
  37. 273
  38. 249
  39. 54
  40. 6

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