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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 543 · 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 1 written when you write all the numbers from 1 to 92? (a) 21 (b) 9 (c) 19 (d) 20
  2. 2.How many times is the digit 9 written when you write all the numbers from 1 to 62? (a) 6 (b) 7 (c) 4 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 5 (b) 16 (c) 15 (d) 17
  6. 6.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7
  7. 7.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 307 (b) 306 (c) 276 (d) 297
  8. 8.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 420 (c) 358 (d) 430
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 6 (b) 3 (c) 5 (d) 4
  10. 10.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) 207 (c) 72 (d) 69
  11. 11.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  12. 12.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) 36 (c) 33 (d) 99
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 3 (d) 2
  14. 14.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 397 (b) 336 (c) 387 (d) 396
  15. 15.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) 12 (b) 36 (c) 108 (d) 39
  16. 16.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 20 (b) 63 (c) 60 (d) 180
  17. 17.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 131 (c) 140 (d) 132
  18. 18.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) 8 (b) 24 (c) 27 (d) 72
  19. 19.How many times is the digit 5 written when you write all the numbers from 1 to 37? (a) 3 (b) 4 (c) 2 (d) 5
  20. 20.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 133 (c) 142 (d) 134
  21. 21.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 106 (c) 88 (d) 97
  22. 22.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 12 (b) 8 (c) 10 (d) 13
  23. 23.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 337 (c) 336 (d) 327
  24. 24.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 154 (c) 172 (d) 163
  25. 25.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) 27 (b) 30 (c) 9 (d) 81
  26. 26.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) 117 (b) 13 (c) 39 (d) 42
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 3 (d) 1
  28. 28.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 523 (c) 522 (d) 420
  29. 29.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 4 (b) 5 (c) 6 (d) 3
  30. 30.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  31. 31.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 5 (b) 6 (c) 4 (d) 7
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 6 (b) 16 (c) 17 (d) 15
  33. 33.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 222 (c) 231 (d) 232
  34. 34.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) 48 (b) 45 (c) 135 (d) 15
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 18 (b) 19 (c) 20 (d) 9
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 16 (b) 6 (c) 17 (d) 18
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 5 (b) 15 (c) 14 (d) 16
  38. 38.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 477 (c) 478 (d) 390
  39. 39.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  40. 40.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4

Answer key

  1. 20
  2. 6
  3. 8
  4. 4
  5. 16
  6. 7
  7. 306
  8. 429
  9. 5
  10. 69
  11. 7
  12. 33
  13. 3
  14. 396
  15. 36
  16. 60
  17. 131
  18. 24
  19. 4
  20. 133
  21. 97
  22. 12
  23. 336
  24. 163
  25. 27
  26. 39
  27. 3
  28. 522
  29. 5
  30. 6
  31. 6
  32. 16
  33. 231
  34. 45
  35. 19
  36. 17
  37. 15
  38. 477
  39. 5
  40. 3

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