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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 242 · 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 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 313 (b) 312 (c) 280 (d) 303
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 96? (a) 20 (b) 18 (c) 9 (d) 19
  3. 3.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 62 (c) 53 (d) 54
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 18 (b) 16 (c) 7 (d) 17
  6. 6.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 279 (c) 270 (d) 280
  7. 7.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) 72 (b) 24 (c) 8 (d) 27
  8. 8.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 170 (c) 179 (d) 188
  9. 9.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) 69 (c) 207 (d) 72
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 4 (b) 6 (c) 3 (d) 5
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  12. 12.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 376 (c) 457 (d) 447
  13. 13.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 173 (c) 182 (d) 174
  14. 14.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 120 (c) 112 (d) 111
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 21 (d) 20
  16. 16.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) 51 (b) 153 (c) 54 (d) 17
  17. 17.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 32 (c) 41 (d) 42
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 5 (b) 2 (c) 3 (d) 4
  19. 19.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) 30 (b) 27 (c) 9 (d) 81
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 18 (d) 20
  21. 21.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  22. 22.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 489 (c) 490 (d) 480
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 45? (a) 5 (b) 6 (c) 3 (d) 4
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  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) 576 (b) 462 (c) 585 (d) 586
  26. 26.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) 69 (b) 22 (c) 198 (d) 66
  27. 27.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) 135 (b) 15 (c) 48 (d) 45
  28. 28.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) 74 (c) 73 (d) 82
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 4 (b) 13 (c) 14 (d) 15
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 9 (d) 19
  31. 31.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
  32. 32.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) 54 (d) 57
  33. 33.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 210 (c) 218 (d) 219
  34. 34.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 130 (c) 129 (d) 120
  35. 35.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) 39 (b) 108 (c) 36 (d) 12
  36. 36.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  37. 37.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) 42 (b) 13 (c) 117 (d) 39
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 8 (b) 19 (c) 18 (d) 17
  39. 39.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) 60 (c) 19 (d) 57
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 18 (b) 19 (c) 8 (d) 20

Answer key

  1. 312
  2. 19
  3. 53
  4. 8
  5. 17
  6. 279
  7. 24
  8. 179
  9. 69
  10. 5
  11. 9
  12. 456
  13. 173
  14. 111
  15. 20
  16. 51
  17. 41
  18. 4
  19. 27
  20. 19
  21. 4
  22. 489
  23. 5
  24. 5
  25. 585
  26. 66
  27. 45
  28. 73
  29. 14
  30. 19
  31. 18
  32. 54
  33. 219
  34. 129
  35. 36
  36. 5
  37. 39
  38. 18
  39. 57
  40. 19

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