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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 913 · 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.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) 57 (b) 19 (c) 60 (d) 171
  2. 2.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 64 (c) 82 (d) 73
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 16 (b) 5 (c) 17 (d) 15
  4. 4.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) 39 (c) 12 (d) 108
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 17 (b) 18 (c) 16 (d) 6
  6. 6.A book has 36 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 72 (c) 63 (d) 64
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 3 (b) 4 (c) 6 (d) 5
  8. 8.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 304 (c) 294 (d) 274
  9. 9.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 7 (c) 8 (d) 13
  10. 10.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) 45 (b) 48 (c) 15 (d) 135
  11. 11.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) 14 (b) 126 (c) 42 (d) 45
  12. 12.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  13. 13.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 456 (c) 382 (d) 465
  14. 14.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) 50 (c) 41 (d) 32
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 32? (a) 1 (b) 4 (c) 3 (d) 2
  16. 16.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) 33 (b) 10 (c) 90 (d) 30
  17. 17.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  18. 18.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 574 (b) 573 (c) 564 (d) 454
  19. 19.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 174 (c) 156 (d) 165
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 16 (b) 17 (c) 15 (d) 6
  21. 21.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 180 (c) 190 (d) 189
  22. 22.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) 72 (c) 27 (d) 24
  23. 23.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
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 10 (b) 9 (c) 8 (d) 3
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 14 (b) 16 (c) 4 (d) 15
  27. 27.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  28. 28.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) 88 (c) 98 (d) 97
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 9 (b) 21 (c) 20 (d) 19
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 18 (b) 6 (c) 17 (d) 16
  31. 31.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  32. 32.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 33 (c) 11 (d) 36
  33. 33.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 495 (b) 504 (c) 408 (d) 505
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 14 (b) 12 (c) 13 (d) 3
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 61? (a) 6 (b) 5 (c) 4 (d) 7
  36. 36.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  37. 37.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 340 (b) 298 (c) 330 (d) 339
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 5 (d) 4
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 51? (a) 4 (b) 5 (c) 3 (d) 6
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 15 (b) 16 (c) 5 (d) 14

Answer key

  1. 57
  2. 73
  3. 16
  4. 36
  5. 17
  6. 63
  7. 5
  8. 303
  9. 7
  10. 45
  11. 42
  12. 3
  13. 465
  14. 41
  15. 3
  16. 30
  17. 6
  18. 573
  19. 165
  20. 16
  21. 189
  22. 24
  23. 21
  24. 3
  25. 9
  26. 15
  27. 9
  28. 97
  29. 20
  30. 17
  31. 5
  32. 33
  33. 504
  34. 13
  35. 6
  36. 7
  37. 339
  38. 5
  39. 5
  40. 15

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