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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 391 · 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 32? (a) 1 (b) 4 (c) 2 (d) 3
  2. 2.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 573 (c) 583 (d) 460
  3. 3.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 408 (c) 505 (d) 495
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 15 (b) 14 (c) 13 (d) 4
  5. 5.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 283 (b) 260 (c) 282 (d) 273
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 36? (a) 3 (b) 4 (c) 5 (d) 2
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 35? (a) 1 (b) 3 (c) 2 (d) 4
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 4 (b) 5 (c) 7 (d) 6
  9. 9.A book has 104 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 205 (b) 208 (c) 195 (d) 204
  10. 10.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 132 (c) 123 (d) 114
  11. 11.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) 90 (b) 30 (c) 33 (d) 10
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 20 (b) 18 (c) 8 (d) 19
  13. 13.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 241 (b) 232 (c) 240 (d) 231
  14. 14.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  15. 15.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) 39 (c) 117 (d) 13
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 18 (b) 20 (c) 19 (d) 9
  17. 17.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  18. 18.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 32 (c) 41 (d) 50
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 19 (d) 18
  20. 20.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 450 (c) 568 (d) 567
  21. 21.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) 27 (c) 72 (d) 24
  22. 22.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 448 (c) 447 (d) 370
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 57? (a) 4 (b) 3 (c) 6 (d) 5
  24. 24.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 206 (c) 201 (d) 202
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 44? (a) 16 (b) 14 (c) 15 (d) 4
  26. 26.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) 63 (c) 20 (d) 60
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 5 (d) 4
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 50? (a) 4 (b) 7 (c) 5 (d) 6
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 19 (b) 18 (c) 8 (d) 20
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 19 (b) 18 (c) 9 (d) 20
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 4 (d) 3
  32. 32.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  33. 33.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) 72 (c) 24 (d) 216
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 5 (b) 16 (c) 17 (d) 15
  35. 35.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 159 (c) 160 (d) 150
  36. 36.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) 21 (b) 189 (c) 66 (d) 63
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 14 (b) 15 (c) 4 (d) 16
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 17 (b) 16 (c) 5 (d) 15
  39. 39.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) 52 (c) 42 (d) 51
  40. 40.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) 51 (b) 144 (c) 16 (d) 48

Answer key

  1. 3
  2. 582
  3. 504
  4. 14
  5. 282
  6. 4
  7. 3
  8. 6
  9. 204
  10. 123
  11. 30
  12. 19
  13. 240
  14. 9
  15. 39
  16. 19
  17. 4
  18. 41
  19. 18
  20. 567
  21. 24
  22. 447
  23. 5
  24. 201
  25. 15
  26. 60
  27. 4
  28. 6
  29. 19
  30. 19
  31. 4
  32. 8
  33. 72
  34. 16
  35. 159
  36. 63
  37. 15
  38. 16
  39. 51
  40. 48

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