← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 854 · 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 98? (a) 9 (b) 19 (c) 20 (d) 21
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 78? (a) 7 (b) 19 (c) 17 (d) 18
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 82? (a) 18 (b) 19 (c) 17 (d) 8
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 9 (b) 8 (c) 6 (d) 7
  5. 5.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) 189 (b) 21 (c) 66 (d) 63
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 4 (b) 2 (c) 3 (d) 5
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 36? (a) 3 (b) 1 (c) 4 (d) 2
  8. 8.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) 69 (d) 198
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 3 (d) 2
  10. 10.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 6 (d) 14
  11. 11.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  12. 12.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
  13. 13.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) 207 (b) 72 (c) 69 (d) 23
  14. 14.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) 45 (b) 15 (c) 18 (d) 5
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 1 (d) 4
  16. 16.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  17. 17.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  18. 18.A book has 122 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 259 (b) 244 (c) 258 (d) 249
  19. 19.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  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) 180 (b) 20 (c) 63 (d) 60
  21. 21.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) 117 (c) 42 (d) 39
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 3 (d) 4
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 20 (b) 9 (c) 19 (d) 21
  24. 24.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) 57 (c) 162 (d) 18
  25. 25.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 134 (c) 125 (d) 126
  26. 26.How many times is the digit 3 written when you write all the numbers from 1 to 69? (a) 17 (b) 6 (c) 16 (d) 18
  27. 27.A book has 91 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 182 (c) 173 (d) 174
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  29. 29.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 528 (b) 529 (c) 424 (d) 519
  30. 30.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) 36 (c) 12 (d) 39
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 15 (b) 13 (c) 14 (d) 3
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 4 (b) 3 (c) 6 (d) 5
  33. 33.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 510 (c) 520 (d) 519
  34. 34.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 77 (b) 78 (c) 68 (d) 86
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 6 (b) 4 (c) 3 (d) 5
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 10 (b) 4 (c) 11 (d) 9
  37. 37.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 28 (b) 38 (c) 37 (d) 46
  38. 38.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 8 (b) 18 (c) 20 (d) 19
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 20 (b) 8 (c) 18 (d) 19
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 16 (d) 17

Answer key

  1. 20
  2. 18
  3. 18
  4. 8
  5. 63
  6. 4
  7. 3
  8. 66
  9. 3
  10. 6
  11. 5
  12. 4
  13. 69
  14. 15
  15. 3
  16. 6
  17. 5
  18. 258
  19. 7
  20. 60
  21. 39
  22. 3
  23. 20
  24. 54
  25. 125
  26. 17
  27. 173
  28. 4
  29. 528
  30. 36
  31. 14
  32. 5
  33. 519
  34. 77
  35. 5
  36. 10
  37. 37
  38. 19
  39. 19
  40. 16

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad