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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 220 · 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 7 written when you write all the numbers from 1 to 77? (a) 17 (b) 16 (c) 7 (d) 15
  2. 2.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
  3. 3.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) 108 (b) 12 (c) 39 (d) 36
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 8 (b) 19 (c) 20 (d) 18
  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) 282 (b) 283 (c) 260 (d) 273
  6. 6.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 573 (c) 574 (d) 564
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 53? (a) 3 (b) 4 (c) 5 (d) 6
  8. 8.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 150 (c) 168 (d) 159
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 1 (b) 2 (c) 3 (d) 4
  10. 10.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) 33 (c) 10 (d) 30
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 59? (a) 15 (b) 17 (c) 5 (d) 16
  12. 12.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  13. 13.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) 63 (b) 60 (c) 20 (d) 180
  14. 14.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) 66 (b) 63 (c) 189 (d) 21
  15. 15.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) 19 (b) 60 (c) 171 (d) 57
  16. 16.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) 54 (c) 153 (d) 17
  17. 17.A book has 207 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 513 (b) 514 (c) 504 (d) 414
  18. 18.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 19 (b) 9 (c) 20 (d) 21
  20. 20.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 286 (b) 312 (c) 321 (d) 322
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 5 (d) 4
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 3 (d) 4
  23. 23.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  24. 24.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
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 62? (a) 7 (b) 6 (c) 9 (d) 10
  26. 26.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 519 (c) 510 (d) 520
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 20 (b) 18 (c) 8 (d) 19
  28. 28.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 15 (b) 16 (c) 14 (d) 4
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  31. 31.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 128 (c) 137 (d) 146
  32. 32.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
  33. 33.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 7 (c) 10 (d) 9
  34. 34.A book has 101 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 202 (b) 195 (c) 196 (d) 186
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 58? (a) 5 (b) 4 (c) 7 (d) 6
  36. 36.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 2 (b) 4 (c) 3 (d) 5
  38. 38.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) 45 (c) 42 (d) 126
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 15 (b) 14 (c) 4 (d) 16
  40. 40.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 81 (c) 30 (d) 9

Answer key

  1. 16
  2. 41
  3. 36
  4. 19
  5. 282
  6. 573
  7. 5
  8. 159
  9. 3
  10. 30
  11. 16
  12. 3
  13. 60
  14. 63
  15. 57
  16. 51
  17. 513
  18. 5
  19. 20
  20. 321
  21. 5
  22. 3
  23. 9
  24. 24
  25. 9
  26. 519
  27. 19
  28. 6
  29. 15
  30. 3
  31. 137
  32. 369
  33. 8
  34. 195
  35. 6
  36. 8
  37. 4
  38. 42
  39. 15
  40. 27

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