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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 200 · 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 two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 65? (a) 16 (b) 6 (c) 17 (d) 18
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 2 (b) 4 (c) 5 (d) 3
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 4 (b) 3 (c) 6 (d) 5
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 5 (d) 4
  6. 6.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) 6 (c) 21 (d) 54
  7. 7.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) 144 (c) 16 (d) 48
  8. 8.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) 72 (b) 69 (c) 207 (d) 23
  9. 9.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 494 (b) 634 (c) 624 (d) 633
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 13 (c) 7 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 3 (d) 2
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 18 (d) 8
  13. 13.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) 126 (d) 42
  14. 14.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 151 (c) 152 (d) 160
  15. 15.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) 153 (b) 17 (c) 51 (d) 54
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 4 (b) 5 (c) 3 (d) 2
  17. 17.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) 48 (b) 15 (c) 135 (d) 45
  18. 18.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 7 (d) 6
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 16 (b) 17 (c) 5 (d) 15
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 61? (a) 5 (b) 7 (c) 6 (d) 4
  21. 21.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 97 (b) 98 (c) 106 (d) 88
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 18 (b) 9 (c) 20 (d) 19
  23. 23.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 150 (c) 140 (d) 149
  24. 24.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 40 (c) 49 (d) 50
  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) 27 (c) 30 (d) 9
  26. 26.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
  27. 27.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 156 (b) 164 (c) 155 (d) 146
  28. 28.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  29. 29.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 387 (c) 388 (d) 330
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 5 (d) 4
  31. 31.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 7 (b) 16 (c) 17 (d) 15
  32. 32.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 16 (b) 14 (c) 4 (d) 15
  34. 34.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 4 (b) 5 (c) 2 (d) 3
  35. 35.How many times is the digit 8 written when you write all the numbers from 1 to 41? (a) 2 (b) 5 (c) 4 (d) 3
  36. 36.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
  37. 37.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  38. 38.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 133 (c) 124 (d) 134
  39. 39.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) 10 (b) 33 (c) 30 (d) 90
  40. 40.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) 63 (c) 20 (d) 180

Answer key

  1. 5
  2. 17
  3. 4
  4. 5
  5. 5
  6. 18
  7. 48
  8. 69
  9. 633
  10. 7
  11. 3
  12. 19
  13. 42
  14. 151
  15. 51
  16. 4
  17. 45
  18. 6
  19. 16
  20. 6
  21. 97
  22. 19
  23. 149
  24. 49
  25. 27
  26. 24
  27. 155
  28. 5
  29. 387
  30. 4
  31. 16
  32. 6
  33. 15
  34. 4
  35. 4
  36. 63
  37. 3
  38. 133
  39. 30
  40. 60

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