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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 393 · 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 6 written when you write all the numbers from 1 to 48? (a) 6 (b) 3 (c) 5 (d) 4
  2. 2.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 238 (b) 230 (c) 237 (d) 228
  3. 3.How many times is the digit 8 written when you write all the numbers from 1 to 53? (a) 6 (b) 4 (c) 5 (d) 3
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 3 (b) 2 (c) 4 (d) 5
  5. 5.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 402 (c) 412 (d) 411
  6. 6.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 325 (b) 324 (c) 288 (d) 315
  7. 7.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 10 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  9. 9.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 44 (c) 26 (d) 35
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 7 (d) 19
  11. 11.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) 5 (b) 15 (c) 45 (d) 18
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 4 (b) 14 (c) 16 (d) 15
  13. 13.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  14. 14.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 442 (c) 432 (d) 441
  15. 15.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  16. 16.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 5 (b) 2 (c) 3 (d) 4
  17. 17.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) 15 (c) 45 (d) 135
  18. 18.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 97 (c) 88 (d) 98
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 6 (b) 3 (c) 4 (d) 5
  20. 20.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) 153 (b) 17 (c) 54 (d) 51
  21. 21.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 166 (c) 174 (d) 165
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 8 (b) 10 (c) 3 (d) 9
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 8 (b) 5 (c) 6 (d) 7
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 8 (b) 9 (c) 7 (d) 6
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 98? (a) 20 (b) 9 (c) 19 (d) 21
  26. 26.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 5 (b) 3 (c) 2 (d) 4
  27. 27.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 18 (b) 17 (c) 19 (d) 8
  28. 28.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) 126 (b) 45 (c) 42 (d) 14
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 4 (b) 6 (c) 3 (d) 5
  30. 30.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) 27 (d) 8
  31. 31.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) 180 (b) 60 (c) 20 (d) 63
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 43? (a) 15 (b) 16 (c) 14 (d) 4
  33. 33.A book has 125 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 268 (c) 267 (d) 250
  34. 34.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) 117 (c) 13 (d) 39
  35. 35.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  36. 36.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 46 (c) 45 (d) 36
  37. 37.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 77 (c) 68 (d) 78
  38. 38.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) 12 (d) 36
  39. 39.A book has 138 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 276 (c) 307 (d) 306
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8

Answer key

  1. 5
  2. 237
  3. 5
  4. 4
  5. 411
  6. 324
  7. 5
  8. 9
  9. 35
  10. 18
  11. 15
  12. 15
  13. 2
  14. 441
  15. 7
  16. 4
  17. 45
  18. 97
  19. 5
  20. 51
  21. 165
  22. 9
  23. 7
  24. 8
  25. 20
  26. 4
  27. 18
  28. 42
  29. 5
  30. 24
  31. 60
  32. 15
  33. 267
  34. 39
  35. 6
  36. 45
  37. 77
  38. 36
  39. 306
  40. 7

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