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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 549 · 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 77? (a) 19 (b) 17 (c) 7 (d) 18
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 3 (b) 13 (c) 14 (d) 15
  3. 3.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 2 (d) 4
  4. 4.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  5. 5.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) 189 (b) 66 (c) 21 (d) 63
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 4 (d) 15
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 14 (b) 16 (c) 15 (d) 4
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 21 (d) 20
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 18 (b) 6 (c) 16 (d) 17
  10. 10.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 7 (d) 5
  11. 11.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 367 (c) 366 (d) 357
  12. 12.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 84 (c) 92 (d) 83
  13. 13.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) 36 (b) 12 (c) 39 (d) 108
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 7 (b) 16 (c) 18 (d) 17
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 15 (b) 16 (c) 5 (d) 17
  16. 16.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 73 (b) 82 (c) 74 (d) 64
  17. 17.The numbers 3 to 11 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) 24 (c) 7 (d) 63
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 17 (b) 6 (c) 18 (d) 16
  19. 19.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 315 (c) 325 (d) 288
  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) 51 (b) 17 (c) 153 (d) 54
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 71? (a) 5 (b) 6 (c) 7 (d) 8
  22. 22.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 15 (d) 5
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  24. 24.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 540 (b) 531 (c) 432 (d) 541
  25. 25.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 57 (c) 60 (d) 19
  26. 26.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 15 (b) 14 (c) 4 (d) 16
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 3 (d) 4
  29. 29.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 110 (c) 118 (d) 100
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 11 (b) 8 (c) 12 (d) 9
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 1 (b) 3 (c) 2 (d) 4
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 9 (b) 17 (c) 18 (d) 15
  33. 33.How many times is the digit 9 written when you write all the numbers from 1 to 43? (a) 3 (b) 5 (c) 2 (d) 4
  34. 34.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) 54 (b) 57 (c) 18 (d) 162
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 54? (a) 6 (b) 5 (c) 3 (d) 4
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 4 (b) 6 (c) 3 (d) 5
  37. 37.A book has 159 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 370 (b) 369 (c) 318 (d) 360
  38. 38.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 258 (b) 270 (c) 280 (d) 279
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 7 (b) 19 (c) 18 (d) 17
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 2 (b) 4 (c) 1 (d) 3

Answer key

  1. 18
  2. 14
  3. 3
  4. 8
  5. 63
  6. 15
  7. 15
  8. 20
  9. 17
  10. 6
  11. 366
  12. 83
  13. 36
  14. 17
  15. 16
  16. 73
  17. 21
  18. 17
  19. 324
  20. 51
  21. 7
  22. 5
  23. 3
  24. 540
  25. 57
  26. 7
  27. 15
  28. 5
  29. 109
  30. 11
  31. 3
  32. 17
  33. 4
  34. 54
  35. 5
  36. 5
  37. 369
  38. 279
  39. 18
  40. 3

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