← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 109 · 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 42? (a) 15 (b) 4 (c) 14 (d) 13
  2. 2.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 2 (d) 3
  3. 3.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) 16 (b) 144 (c) 51 (d) 48
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 77? (a) 7 (b) 19 (c) 17 (d) 18
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 19 (d) 9
  6. 6.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 3 (d) 4
  7. 7.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 194 (b) 176 (c) 185 (d) 186
  8. 8.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) 19 (b) 171 (c) 57 (d) 60
  9. 9.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) 15 (b) 18 (c) 5 (d) 45
  10. 10.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) 20 (c) 180 (d) 63
  11. 11.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 183 (c) 200 (d) 193
  12. 12.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 5 (d) 3
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 37? (a) 4 (b) 2 (c) 3 (d) 1
  14. 14.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) 21 (b) 63 (c) 7 (d) 24
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 32? (a) 15 (b) 3 (c) 14 (d) 13
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  17. 17.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) 17 (b) 51 (c) 153 (d) 54
  18. 18.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) 69 (b) 207 (c) 23 (d) 72
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  20. 20.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) 75 (c) 72 (d) 24
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 73? (a) 7 (b) 18 (c) 17 (d) 19
  22. 22.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 14 (b) 13 (c) 15 (d) 3
  24. 24.A book has 194 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 388 (b) 475 (c) 474 (d) 465
  25. 25.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 38 (b) 56 (c) 47 (d) 48
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 81? (a) 17 (b) 18 (c) 8 (d) 19
  27. 27.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) 39 (b) 42 (c) 117 (d) 13
  28. 28.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 138 (b) 129 (c) 120 (d) 130
  29. 29.A book has 139 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 310 (b) 300 (c) 309 (d) 278
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 19 (d) 18
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 35? (a) 15 (b) 13 (c) 3 (d) 14
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 17 (d) 16
  33. 33.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 2 (d) 10
  34. 34.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 417 (c) 418 (d) 350
  35. 35.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 16 (b) 5 (c) 17 (d) 15
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 36? (a) 3 (b) 13 (c) 14 (d) 15
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 3 (b) 2 (c) 4 (d) 5
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 5 (b) 7 (c) 6 (d) 4
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 17 (b) 8 (c) 19 (d) 18

Answer key

  1. 14
  2. 2
  3. 48
  4. 18
  5. 19
  6. 4
  7. 185
  8. 57
  9. 15
  10. 60
  11. 192
  12. 4
  13. 3
  14. 21
  15. 14
  16. 3
  17. 51
  18. 69
  19. 7
  20. 72
  21. 18
  22. 4
  23. 14
  24. 474
  25. 47
  26. 18
  27. 39
  28. 129
  29. 309
  30. 18
  31. 14
  32. 17
  33. 2
  34. 417
  35. 7
  36. 16
  37. 14
  38. 4
  39. 6
  40. 18

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