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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 682 · 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 45? (a) 4 (b) 2 (c) 5 (d) 3
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 14 (b) 15 (c) 13 (d) 3
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 17 (b) 15 (c) 5 (d) 16
  4. 4.A book has 80 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 160 (c) 142 (d) 151
  5. 5.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 8 (c) 11 (d) 9
  6. 6.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  7. 7.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  9. 9.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 292 (c) 330 (d) 331
  10. 10.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) 135 (c) 15 (d) 45
  11. 11.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 80 (c) 88 (d) 79
  12. 12.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
  13. 13.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 577 (b) 456 (c) 576 (d) 567
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 19 (d) 17
  15. 15.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 142 (c) 124 (d) 133
  16. 16.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  17. 17.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) 75 (b) 72 (c) 216 (d) 24
  18. 18.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  19. 19.The numbers 7 to 15 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 99 (b) 33 (c) 11 (d) 36
  20. 20.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) 180 (d) 20
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 9 (c) 8 (d) 11
  22. 22.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 15 (b) 3 (c) 14 (d) 13
  23. 23.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  24. 24.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) 23 (b) 207 (c) 72 (d) 69
  25. 25.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
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 80? (a) 17 (b) 19 (c) 18 (d) 8
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 3 (b) 2 (c) 1 (d) 4
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 66? (a) 6 (b) 17 (c) 18 (d) 16
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 4 (b) 15 (c) 14 (d) 13
  30. 30.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
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 7 (d) 18
  32. 32.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 2 (b) 3 (c) 4 (d) 1
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 4 (b) 3 (c) 2 (d) 5
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 33? (a) 13 (b) 3 (c) 14 (d) 15
  35. 35.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 6 (c) 10 (d) 4
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 17 (b) 7 (c) 18 (d) 16
  37. 37.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) 30 (b) 9 (c) 81 (d) 27
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 18 (b) 20 (c) 8 (d) 19
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 48? (a) 4 (b) 13 (c) 14 (d) 15
  40. 40.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 158 (c) 140 (d) 149

Answer key

  1. 4
  2. 14
  3. 16
  4. 151
  5. 9
  6. 2
  7. 8
  8. 6
  9. 330
  10. 45
  11. 79
  12. 21
  13. 576
  14. 18
  15. 133
  16. 4
  17. 72
  18. 7
  19. 33
  20. 60
  21. 9
  22. 14
  23. 2
  24. 69
  25. 63
  26. 18
  27. 3
  28. 17
  29. 14
  30. 19
  31. 18
  32. 3
  33. 4
  34. 14
  35. 5
  36. 17
  37. 27
  38. 19
  39. 14
  40. 149

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