← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 38 · 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 4 written when you write all the numbers from 1 to 56? (a) 16 (b) 17 (c) 5 (d) 15
  2. 2.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 61 (b) 70 (c) 62 (d) 52
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 83? (a) 19 (b) 18 (c) 17 (d) 8
  4. 4.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  5. 5.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 20 (b) 18 (c) 8 (d) 19
  6. 6.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 8 (c) 24 (d) 72
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 72? (a) 18 (b) 17 (c) 19 (d) 7
  8. 8.The numbers 2 to 10 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 6 (b) 18 (c) 21 (d) 54
  9. 9.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 100 (c) 118 (d) 109
  10. 10.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  11. 11.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 58? (a) 4 (b) 7 (c) 5 (d) 6
  13. 13.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 249 (b) 238 (c) 250 (d) 240
  14. 14.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) 33 (b) 11 (c) 99 (d) 36
  15. 15.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 466 (c) 465 (d) 382
  16. 16.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 42 (b) 126 (c) 45 (d) 14
  17. 17.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) 21 (b) 63 (c) 189 (d) 66
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 70? (a) 16 (b) 17 (c) 7 (d) 18
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 20 (b) 18 (c) 19 (d) 8
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 7 (b) 8 (c) 6 (d) 5
  21. 21.A book has 74 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 139 (b) 130 (c) 140 (d) 148
  22. 22.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) 15 (b) 48 (c) 135 (d) 45
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 17 (b) 6 (c) 16 (d) 18
  24. 24.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 1 (c) 10 (d) 3
  25. 25.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 126 (c) 118 (d) 117
  26. 26.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 583 (c) 460 (d) 573
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 34? (a) 1 (b) 3 (c) 2 (d) 4
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 8 (d) 17
  30. 30.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
  31. 31.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 218 (b) 219 (c) 220 (d) 210
  32. 32.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 172 (c) 171 (d) 162
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 45? (a) 4 (b) 11 (c) 12 (d) 10
  34. 34.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  35. 35.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) 21 (c) 24 (d) 7
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 6 (b) 8 (c) 7 (d) 5
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 4 (b) 6 (c) 5 (d) 3
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 19 (b) 18 (c) 9 (d) 20
  39. 39.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) 54 (b) 17 (c) 153 (d) 51
  40. 40.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 558 (b) 567 (c) 450 (d) 568

Answer key

  1. 16
  2. 61
  3. 18
  4. 2
  5. 19
  6. 24
  7. 18
  8. 18
  9. 109
  10. 7
  11. 3
  12. 6
  13. 249
  14. 33
  15. 465
  16. 42
  17. 63
  18. 17
  19. 19
  20. 7
  21. 139
  22. 45
  23. 17
  24. 2
  25. 117
  26. 582
  27. 3
  28. 4
  29. 18
  30. 69
  31. 219
  32. 171
  33. 11
  34. 5
  35. 21
  36. 7
  37. 5
  38. 19
  39. 51
  40. 567

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