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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 892 · 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 3 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 17 (d) 6
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 5 (d) 2
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 18 (d) 17
  4. 4.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  5. 5.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  6. 6.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 4 (b) 5 (c) 3 (d) 2
  8. 8.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 309 (c) 310 (d) 278
  9. 9.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) 15 (c) 48 (d) 45
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 47? (a) 15 (b) 14 (c) 16 (d) 4
  12. 12.A book has 112 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 229 (b) 219 (c) 224 (d) 228
  13. 13.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  14. 14.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) 19 (c) 57 (d) 60
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 6 (b) 18 (c) 16 (d) 17
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 17 (b) 19 (c) 8 (d) 18
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  18. 18.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  20. 20.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 568 (b) 567 (c) 558 (d) 450
  21. 21.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) 39 (c) 36 (d) 12
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 5 (b) 4 (c) 3 (d) 6
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 5 (b) 8 (c) 7 (d) 6
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 18 (b) 17 (c) 19 (d) 8
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 5 (b) 4 (c) 2 (d) 3
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 20 (d) 18
  27. 27.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 158 (c) 166 (d) 157
  28. 28.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) 75 (c) 72 (d) 216
  29. 29.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  30. 30.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 20 (b) 9 (c) 19 (d) 18
  31. 31.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 60? (a) 16 (b) 15 (c) 17 (d) 6
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 65? (a) 16 (b) 6 (c) 17 (d) 18
  34. 34.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 198 (c) 199 (d) 189
  35. 35.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 62 (c) 44 (d) 53
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 97? (a) 17 (b) 18 (c) 15 (d) 9
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 5 (d) 10
  38. 38.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 10 (b) 8 (c) 11 (d) 7
  39. 39.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 155 (c) 146 (d) 156
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 2 (d) 1

Answer key

  1. 17
  2. 4
  3. 18
  4. 3
  5. 8
  6. 6
  7. 4
  8. 309
  9. 45
  10. 7
  11. 15
  12. 228
  13. 9
  14. 57
  15. 17
  16. 18
  17. 3
  18. 5
  19. 7
  20. 567
  21. 36
  22. 5
  23. 7
  24. 18
  25. 4
  26. 19
  27. 157
  28. 72
  29. 6
  30. 19
  31. 8
  32. 16
  33. 17
  34. 198
  35. 53
  36. 17
  37. 5
  38. 10
  39. 155
  40. 3

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