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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 921 · 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 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 72 (c) 71 (d) 80
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 20 (d) 9
  4. 4.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  5. 5.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 51 (c) 42 (d) 52
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 4 (b) 6 (c) 3 (d) 5
  7. 7.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) 75 (b) 216 (c) 24 (d) 72
  8. 8.A book has 203 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 502 (c) 501 (d) 406
  9. 9.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) 36 (c) 108 (d) 12
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 19 (b) 7 (c) 18 (d) 17
  11. 11.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  13. 13.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 465 (c) 474 (d) 475
  14. 14.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 252 (c) 243 (d) 253
  15. 15.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  16. 16.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) 81 (b) 9 (c) 30 (d) 27
  17. 17.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 188 (c) 180 (d) 179
  18. 18.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) 153 (c) 51 (d) 54
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 3 (d) 10
  20. 20.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 363 (c) 314 (d) 354
  21. 21.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 11 (d) 10
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 4 (b) 14 (c) 15 (d) 16
  25. 25.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) 24 (c) 7 (d) 21
  26. 26.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  27. 27.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 298 (c) 297 (d) 270
  28. 28.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 100 (c) 90 (d) 99
  29. 29.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 192 (c) 184 (d) 174
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 14 (b) 16 (c) 15 (d) 4
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 7 (b) 4 (c) 6 (d) 5
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 2 (d) 3
  33. 33.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) 57 (b) 171 (c) 60 (d) 19
  34. 34.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 327 (b) 296 (c) 336 (d) 337
  35. 35.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
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 17 (b) 16 (c) 15 (d) 5
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 71? (a) 7 (b) 17 (c) 16 (d) 18
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 51? (a) 15 (b) 14 (c) 16 (d) 5
  39. 39.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 123 (c) 114 (d) 124
  40. 40.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 349 (c) 339 (d) 348

Answer key

  1. 71
  2. 6
  3. 20
  4. 3
  5. 51
  6. 5
  7. 72
  8. 501
  9. 36
  10. 18
  11. 7
  12. 5
  13. 474
  14. 252
  15. 4
  16. 27
  17. 179
  18. 51
  19. 2
  20. 363
  21. 9
  22. 20
  23. 8
  24. 15
  25. 21
  26. 6
  27. 297
  28. 99
  29. 183
  30. 15
  31. 6
  32. 3
  33. 57
  34. 336
  35. 15
  36. 16
  37. 17
  38. 15
  39. 123
  40. 348

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