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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 532 · 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 55? (a) 15 (b) 16 (c) 17 (d) 5
  2. 2.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 84? (a) 19 (b) 17 (c) 8 (d) 18
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 87? (a) 7 (b) 8 (c) 6 (d) 9
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 14 (b) 13 (c) 15 (d) 4
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 9 (d) 20
  7. 7.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 486 (b) 622 (c) 612 (d) 621
  8. 8.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 8 (d) 18
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 4 (b) 16 (c) 15 (d) 14
  10. 10.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
  11. 11.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) 54 (c) 17 (d) 153
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 20 (d) 19
  13. 13.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 3 (d) 1
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 89? (a) 8 (b) 7 (c) 10 (d) 9
  15. 15.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 555 (c) 448 (d) 565
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 19 (b) 17 (c) 18 (d) 7
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 62? (a) 7 (b) 4 (c) 5 (d) 6
  18. 18.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 264 (b) 274 (c) 273 (d) 254
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 18 (b) 20 (c) 19 (d) 9
  20. 20.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 9 (c) 8 (d) 12
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 11 (b) 9 (c) 8 (d) 12
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 5 (b) 2 (c) 3 (d) 4
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 32? (a) 3 (b) 7 (c) 4 (d) 6
  24. 24.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 63 (b) 64 (c) 72 (d) 54
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 6 (b) 16 (c) 17 (d) 18
  26. 26.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 36 (c) 26 (d) 35
  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) 15 (b) 48 (c) 45 (d) 135
  28. 28.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  29. 29.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 133 (b) 124 (c) 134 (d) 142
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 18 (d) 8
  31. 31.A book has 190 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 380 (b) 463 (c) 453 (d) 462
  32. 32.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 6 (d) 5
  33. 33.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 414 (b) 514 (c) 513 (d) 504
  34. 34.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 202 (c) 192 (d) 201
  35. 35.The numbers 17 to 25 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) 21 (c) 63 (d) 189
  36. 36.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 310 (c) 309 (d) 278
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 96? (a) 19 (b) 20 (c) 9 (d) 21
  38. 38.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 171 (b) 162 (c) 172 (d) 180
  39. 39.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 170 (b) 178 (c) 160 (d) 169
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 17 (c) 6 (d) 16

Answer key

  1. 16
  2. 6
  3. 18
  4. 8
  5. 14
  6. 20
  7. 621
  8. 18
  9. 15
  10. 54
  11. 51
  12. 19
  13. 2
  14. 9
  15. 564
  16. 18
  17. 6
  18. 273
  19. 19
  20. 8
  21. 11
  22. 4
  23. 6
  24. 63
  25. 17
  26. 35
  27. 45
  28. 8
  29. 133
  30. 19
  31. 462
  32. 6
  33. 513
  34. 201
  35. 63
  36. 309
  37. 20
  38. 171
  39. 169
  40. 17

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