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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 471 · 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 9 written when you write all the numbers from 1 to 43? (a) 2 (b) 3 (c) 4 (d) 5
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 17 (b) 19 (c) 8 (d) 18
  3. 3.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 510 (c) 511 (d) 501
  4. 4.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 97 (b) 106 (c) 98 (d) 88
  5. 5.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  6. 6.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 244 (c) 258 (d) 259
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 21 (d) 9
  8. 8.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 406 (c) 405 (d) 342
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  10. 10.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 4 (d) 3
  11. 11.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) 24 (b) 72 (c) 8 (d) 27
  12. 12.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 415 (c) 348 (d) 414
  13. 13.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) 30 (b) 33 (c) 10 (d) 90
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 16 (b) 15 (c) 6 (d) 17
  15. 15.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) 264 (c) 274 (d) 254
  16. 16.The numbers 10 to 18 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) 126 (c) 14 (d) 42
  17. 17.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  18. 18.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 160 (c) 142 (d) 151
  19. 19.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 3 (d) 16
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 7 (b) 18 (c) 17 (d) 19
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 21 (b) 19 (c) 20 (d) 9
  23. 23.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 172 (c) 171 (d) 162
  24. 24.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 403 (c) 402 (d) 340
  25. 25.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 3 (d) 2
  26. 26.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) 42 (c) 41 (d) 32
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 95? (a) 20 (b) 9 (c) 18 (d) 19
  28. 28.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 225 (c) 235 (d) 234
  29. 29.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) 54 (d) 51
  30. 30.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) 135 (c) 15 (d) 45
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 7 (b) 6 (c) 4 (d) 5
  32. 32.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 9 (b) 20 (c) 18 (d) 19
  33. 33.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 68 (c) 59 (d) 60
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 8 (b) 11 (c) 13 (d) 14
  35. 35.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 67? (a) 14 (b) 6 (c) 15 (d) 16
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 9 (b) 19 (c) 20 (d) 21
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 45? (a) 2 (b) 4 (c) 3 (d) 5
  39. 39.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) 144 (b) 16 (c) 51 (d) 48
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 8 (b) 9 (c) 7 (d) 6

Answer key

  1. 4
  2. 18
  3. 510
  4. 97
  5. 9
  6. 258
  7. 20
  8. 405
  9. 4
  10. 3
  11. 24
  12. 414
  13. 30
  14. 16
  15. 273
  16. 42
  17. 9
  18. 151
  19. 2
  20. 4
  21. 18
  22. 20
  23. 171
  24. 402
  25. 2
  26. 41
  27. 19
  28. 234
  29. 51
  30. 45
  31. 6
  32. 19
  33. 59
  34. 13
  35. 8
  36. 15
  37. 20
  38. 4
  39. 48
  40. 8

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