← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 76 · 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 2 written when you write all the numbers from 1 to 54? (a) 17 (b) 5 (c) 16 (d) 15
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 16 (b) 17 (c) 7 (d) 18
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 21 (d) 9
  5. 5.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) 60 (d) 20
  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) 24 (b) 72 (c) 8 (d) 27
  7. 7.How many times is the digit 8 written when you write all the numbers from 1 to 63? (a) 5 (b) 4 (c) 7 (d) 6
  8. 8.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  9. 9.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 231 (c) 226 (d) 222
  10. 10.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 164 (b) 154 (c) 172 (d) 163
  11. 11.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) 99 (d) 33
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 15 (b) 16 (c) 4 (d) 14
  13. 13.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 18 (c) 3 (d) 2
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 65? (a) 13 (b) 10 (c) 12 (d) 6
  15. 15.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) 63 (c) 21 (d) 66
  16. 16.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  17. 17.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 526 (c) 525 (d) 422
  18. 18.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 414 (c) 348 (d) 415
  19. 19.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) 18 (c) 15 (d) 5
  20. 20.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 16 (b) 6 (c) 18 (d) 17
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  22. 22.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) 57 (b) 171 (c) 60 (d) 19
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 17 (d) 16
  24. 24.How many times is the digit 2 written when you write all the numbers from 1 to 63? (a) 16 (b) 18 (c) 17 (d) 6
  25. 25.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 10 (d) 11
  26. 26.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 78 (c) 88 (d) 87
  27. 27.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 4 (c) 15 (d) 5
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 7 (b) 6 (c) 4 (d) 5
  29. 29.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) 72 (b) 216 (c) 75 (d) 24
  30. 30.The numbers 6 to 14 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 30 (b) 10 (c) 33 (d) 90
  31. 31.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 231 (b) 232 (c) 240 (d) 241
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  33. 33.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 5 (c) 7 (d) 6
  34. 34.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 423 (b) 354 (c) 414 (d) 424
  35. 35.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 426 (c) 531 (d) 532
  36. 36.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 3 (b) 4 (c) 5 (d) 2
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 17 (d) 16
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 16 (b) 7 (c) 17 (d) 18
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 3 (b) 6 (c) 4 (d) 5
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 2 (b) 1 (c) 3 (d) 4

Answer key

  1. 16
  2. 17
  3. 2
  4. 20
  5. 60
  6. 24
  7. 6
  8. 4
  9. 231
  10. 163
  11. 33
  12. 15
  13. 2
  14. 12
  15. 63
  16. 7
  17. 525
  18. 414
  19. 15
  20. 17
  21. 3
  22. 57
  23. 17
  24. 17
  25. 9
  26. 87
  27. 5
  28. 6
  29. 72
  30. 30
  31. 240
  32. 5
  33. 6
  34. 423
  35. 531
  36. 4
  37. 16
  38. 17
  39. 5
  40. 3

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