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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 842 · 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 30? (a) 1 (b) 2 (c) 3 (d) 4
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 2 (d) 1
  3. 3.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 11 (d) 10
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  5. 5.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  6. 6.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) 36 (b) 11 (c) 33 (d) 99
  7. 7.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  8. 8.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) 39 (b) 36 (c) 108 (d) 12
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 10 (b) 9 (c) 11 (d) 3
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 19 (b) 17 (c) 18 (d) 7
  11. 11.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) 54 (b) 18 (c) 162 (d) 57
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 13 (b) 11 (c) 8 (d) 14
  13. 13.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) 66 (c) 198 (d) 69
  14. 14.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 42 (c) 39 (d) 117
  15. 15.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 90 (c) 72 (d) 81
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 5 (b) 3 (c) 4 (d) 2
  18. 18.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) 24 (b) 63 (c) 7 (d) 21
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 65? (a) 4 (b) 7 (c) 5 (d) 6
  20. 20.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 98 (c) 97 (d) 106
  21. 21.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 586 (c) 462 (d) 585
  22. 22.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 7 (d) 8
  23. 23.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 372 (c) 326 (d) 381
  24. 24.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  25. 25.A book has 107 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 204 (b) 214 (c) 321 (d) 213
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 73? (a) 6 (b) 5 (c) 8 (d) 7
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 75? (a) 19 (b) 18 (c) 7 (d) 17
  28. 28.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
  29. 29.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 3 (d) 1
  30. 30.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) 72 (c) 75 (d) 24
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 19 (b) 16 (c) 9 (d) 18
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 47? (a) 4 (b) 5 (c) 3 (d) 6
  33. 33.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) 180 (b) 63 (c) 20 (d) 60
  34. 34.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  35. 35.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 103 (c) 94 (d) 104
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 5 (b) 17 (c) 15 (d) 16
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 18 (b) 7 (c) 17 (d) 19
  38. 38.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 154 (c) 136 (d) 145
  39. 39.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 301 (b) 300 (c) 291 (d) 272
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 56? (a) 17 (b) 16 (c) 5 (d) 15

Answer key

  1. 3
  2. 3
  3. 9
  4. 2
  5. 7
  6. 33
  7. 9
  8. 36
  9. 10
  10. 18
  11. 54
  12. 13
  13. 66
  14. 39
  15. 81
  16. 6
  17. 4
  18. 21
  19. 6
  20. 97
  21. 585
  22. 8
  23. 381
  24. 6
  25. 213
  26. 7
  27. 18
  28. 69
  29. 2
  30. 72
  31. 18
  32. 5
  33. 60
  34. 3
  35. 103
  36. 16
  37. 18
  38. 145
  39. 300
  40. 16

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