← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 713 · 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 93? (a) 9 (b) 20 (c) 19 (d) 18
  2. 2.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) 51 (d) 153
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 6 (b) 16 (c) 18 (d) 17
  4. 4.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  5. 5.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 484 (c) 474 (d) 394
  6. 6.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 6 (c) 7 (d) 10
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 14 (d) 15
  8. 8.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 1 (d) 10
  9. 9.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) 72 (b) 27 (c) 24 (d) 8
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 35? (a) 3 (b) 2 (c) 5 (d) 4
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 20 (d) 9
  12. 12.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 4 (d) 3
  13. 13.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 68? (a) 8 (b) 7 (c) 5 (d) 6
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 76? (a) 14 (b) 12 (c) 7 (d) 15
  16. 16.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
  17. 17.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 8 (b) 5 (c) 7 (d) 6
  18. 18.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 390 (c) 477 (d) 478
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 19 (b) 7 (c) 17 (d) 18
  20. 20.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) 60 (c) 57 (d) 171
  21. 21.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 468 (c) 469 (d) 459
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 15 (b) 13 (c) 4 (d) 14
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 16 (b) 6 (c) 17 (d) 18
  24. 24.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 174 (c) 156 (d) 165
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 8 (b) 18 (c) 19 (d) 17
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 35? (a) 13 (b) 15 (c) 3 (d) 14
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 17 (b) 5 (c) 16 (d) 15
  28. 28.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 20 (b) 8 (c) 18 (d) 19
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 34? (a) 1 (b) 2 (c) 3 (d) 4
  30. 30.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) 135 (b) 45 (c) 48 (d) 15
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 7 (b) 19 (c) 17 (d) 18
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 65? (a) 6 (b) 18 (c) 17 (d) 16
  33. 33.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 288 (c) 298 (d) 270
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 93? (a) 14 (b) 9 (c) 11 (d) 13
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 14 (b) 13 (c) 3 (d) 15
  36. 36.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 94 (c) 93 (d) 102
  37. 37.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) 66 (c) 63 (d) 21
  38. 38.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) 21 (b) 6 (c) 54 (d) 18
  39. 39.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) 69 (b) 66 (c) 22 (d) 198
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 14 (b) 12 (c) 13 (d) 3

Answer key

  1. 19
  2. 51
  3. 17
  4. 8
  5. 483
  6. 6
  7. 15
  8. 2
  9. 24
  10. 4
  11. 20
  12. 3
  13. 3
  14. 7
  15. 14
  16. 4
  17. 7
  18. 477
  19. 18
  20. 57
  21. 468
  22. 14
  23. 17
  24. 165
  25. 18
  26. 14
  27. 16
  28. 19
  29. 3
  30. 45
  31. 18
  32. 17
  33. 297
  34. 13
  35. 14
  36. 93
  37. 63
  38. 18
  39. 66
  40. 13

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