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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 893 · 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 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) 24 (c) 27 (d) 72
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 15 (b) 16 (c) 14 (d) 4
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 5 (b) 2 (c) 4 (d) 3
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 91? (a) 12 (b) 10 (c) 9 (d) 11
  5. 5.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) 140 (c) 148 (d) 130
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 2 (b) 3 (c) 4 (d) 1
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 6 (b) 4 (c) 7 (d) 5
  8. 8.How many times is the digit 1 written when you write all the numbers from 1 to 58? (a) 17 (b) 15 (c) 5 (d) 16
  9. 9.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 15 (b) 14 (c) 13 (d) 3
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 8 (d) 7
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 18 (b) 9 (c) 19 (d) 20
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 17 (b) 15 (c) 6 (d) 16
  13. 13.How many times is the digit 2 written when you write all the numbers from 1 to 44? (a) 14 (b) 15 (c) 4 (d) 16
  14. 14.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  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) 171 (b) 60 (c) 19 (d) 57
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 88? (a) 19 (b) 8 (c) 18 (d) 20
  17. 17.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 36 (b) 35 (c) 44 (d) 26
  18. 18.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 396 (c) 397 (d) 387
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 43? (a) 5 (b) 3 (c) 4 (d) 2
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  21. 21.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) 153 (c) 54 (d) 17
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  23. 23.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 5 (b) 4 (c) 3 (d) 2
  24. 24.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) 135 (b) 48 (c) 15 (d) 45
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  26. 26.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  27. 27.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) 22 (b) 198 (c) 66 (d) 69
  28. 28.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 148 (c) 158 (d) 166
  29. 29.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) 216 (b) 24 (c) 72 (d) 75
  30. 30.The numbers 12 to 20 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) 48 (c) 144 (d) 16
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 14 (b) 16 (c) 15 (d) 4
  32. 32.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 604 (c) 474 (d) 603
  33. 33.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) 12 (b) 36 (c) 108 (d) 39
  34. 34.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 31 (b) 40 (c) 32 (d) 22
  35. 35.The numbers 2 to 10 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) 54 (c) 21 (d) 6
  36. 36.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 5 (d) 7
  37. 37.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) 162 (b) 57 (c) 18 (d) 54
  38. 38.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 471 (b) 462 (c) 386 (d) 472
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 84? (a) 18 (b) 20 (c) 8 (d) 19
  40. 40.The numbers 1 to 9 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) 45 (c) 5 (d) 15

Answer key

  1. 24
  2. 15
  3. 4
  4. 11
  5. 139
  6. 3
  7. 6
  8. 16
  9. 14
  10. 7
  11. 19
  12. 16
  13. 15
  14. 4
  15. 57
  16. 19
  17. 35
  18. 396
  19. 4
  20. 6
  21. 51
  22. 5
  23. 4
  24. 45
  25. 5
  26. 9
  27. 66
  28. 157
  29. 72
  30. 48
  31. 15
  32. 603
  33. 36
  34. 31
  35. 18
  36. 6
  37. 54
  38. 471
  39. 19
  40. 15

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