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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 215 · 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 19 to 27 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 207 (b) 23 (c) 72 (d) 69
  2. 2.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) 8 (d) 27
  3. 3.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  4. 4.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 130 (c) 148 (d) 140
  5. 5.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) 60 (b) 180 (c) 20 (d) 63
  6. 6.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  7. 7.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) 72 (b) 75 (c) 24 (d) 216
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 6 (b) 8 (c) 7 (d) 9
  9. 9.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
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 92? (a) 9 (b) 18 (c) 20 (d) 19
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 4 (b) 2 (c) 5 (d) 3
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 46? (a) 16 (b) 14 (c) 4 (d) 15
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 34? (a) 8 (b) 9 (c) 3 (d) 10
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 13 (d) 7
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 6 (b) 17 (c) 15 (d) 16
  16. 16.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 136 (c) 126 (d) 135
  17. 17.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 595 (b) 468 (c) 585 (d) 594
  18. 18.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 4 (b) 2 (c) 3 (d) 5
  20. 20.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 492 (b) 630 (c) 631 (d) 621
  21. 21.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8
  22. 22.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 582 (c) 591 (d) 592
  23. 23.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 447 (c) 456 (d) 457
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 3 (b) 15 (c) 14 (d) 13
  25. 25.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 185 (c) 186 (d) 176
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 88? (a) 8 (b) 18 (c) 20 (d) 19
  27. 27.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 427 (b) 426 (c) 417 (d) 356
  28. 28.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) 63 (b) 24 (c) 7 (d) 21
  29. 29.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 300 (c) 272 (d) 291
  30. 30.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  31. 31.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 66 (b) 69 (c) 198 (d) 22
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 4 (d) 5
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 15 (b) 17 (c) 5 (d) 16
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 19 (b) 8 (c) 20 (d) 18
  35. 35.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) 108 (c) 12 (d) 39
  36. 36.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 134 (c) 125 (d) 126
  37. 37.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 78? (a) 16 (b) 17 (c) 7 (d) 18
  39. 39.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) 18 (b) 162 (c) 57 (d) 54
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 4 (b) 7 (c) 6 (d) 5

Answer key

  1. 69
  2. 24
  3. 3
  4. 139
  5. 60
  6. 5
  7. 72
  8. 8
  9. 14
  10. 19
  11. 4
  12. 15
  13. 9
  14. 7
  15. 16
  16. 135
  17. 594
  18. 6
  19. 4
  20. 630
  21. 8
  22. 591
  23. 456
  24. 14
  25. 185
  26. 19
  27. 426
  28. 21
  29. 300
  30. 9
  31. 66
  32. 4
  33. 16
  34. 19
  35. 36
  36. 125
  37. 8
  38. 17
  39. 54
  40. 6

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