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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 252 · 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 8 written when you write all the numbers from 1 to 44? (a) 3 (b) 5 (c) 4 (d) 2
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 89? (a) 8 (b) 19 (c) 18 (d) 20
  3. 3.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  4. 4.A book has 246 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 492 (c) 631 (d) 630
  5. 5.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) 45 (b) 42 (c) 14 (d) 126
  6. 6.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) 24 (b) 216 (c) 72 (d) 75
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 8 (b) 13 (c) 10 (d) 12
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 5 (d) 6
  9. 9.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 37 (c) 46 (d) 28
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 17 (b) 18 (c) 7 (d) 19
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 17 (b) 5 (c) 15 (d) 16
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 16 (b) 14 (c) 15 (d) 4
  13. 13.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) 24 (b) 8 (c) 27 (d) 72
  14. 14.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) 7 (b) 63 (c) 24 (d) 21
  15. 15.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) 57 (b) 54 (c) 18 (d) 162
  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) 90 (c) 30 (d) 10
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 4 (b) 15 (c) 16 (d) 14
  18. 18.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) 69 (b) 22 (c) 198 (d) 66
  19. 19.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) 21 (c) 189 (d) 63
  20. 20.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 8 (c) 9 (d) 10
  21. 21.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 201 (b) 211 (c) 212 (d) 210
  22. 22.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 184 (c) 183 (d) 192
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 3 (b) 6 (c) 4 (d) 5
  24. 24.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 20 (b) 8 (c) 19 (d) 18
  25. 25.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) 81 (b) 30 (c) 27 (d) 9
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 6 (b) 16 (c) 17 (d) 15
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 20 (d) 18
  28. 28.A book has 117 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 243 (b) 351 (c) 244 (d) 234
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 4 (b) 14 (c) 13 (d) 15
  30. 30.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) 17 (d) 153
  31. 31.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 304 (c) 274 (d) 303
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 17 (b) 6 (c) 16 (d) 18
  33. 33.A book has 210 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 523 (c) 420 (d) 513
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 2 (d) 5
  35. 35.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 522 (c) 531 (d) 532
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 6 (b) 4 (c) 3 (d) 5
  37. 37.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 4 (b) 14 (c) 16 (d) 15
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 16 (b) 15 (c) 6 (d) 17
  40. 40.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9

Answer key

  1. 4
  2. 19
  3. 8
  4. 630
  5. 42
  6. 72
  7. 12
  8. 6
  9. 37
  10. 18
  11. 16
  12. 15
  13. 24
  14. 21
  15. 54
  16. 30
  17. 15
  18. 66
  19. 63
  20. 9
  21. 210
  22. 183
  23. 5
  24. 19
  25. 27
  26. 16
  27. 19
  28. 243
  29. 14
  30. 51
  31. 303
  32. 17
  33. 522
  34. 4
  35. 531
  36. 5
  37. 7
  38. 15
  39. 16
  40. 8

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