← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 967 · 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.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 398 (b) 490 (c) 480 (d) 489
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  3. 3.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  4. 4.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 75 (b) 84 (c) 76 (d) 66
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 17 (b) 7 (c) 16 (d) 18
  6. 6.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 606 (b) 607 (c) 597 (d) 476
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 46? (a) 12 (b) 13 (c) 11 (d) 4
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 75? (a) 8 (b) 7 (c) 6 (d) 5
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 5 (b) 16 (c) 14 (d) 15
  10. 10.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 193 (b) 192 (c) 183 (d) 200
  11. 11.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  12. 12.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 4 (b) 2 (c) 3 (d) 5
  13. 13.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
  14. 14.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) 18 (b) 57 (c) 54 (d) 162
  15. 15.A book has 23 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 37 (b) 46 (c) 38 (d) 28
  16. 16.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) 24 (b) 72 (c) 75 (d) 216
  17. 17.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) 90 (b) 30 (c) 10 (d) 33
  18. 18.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) 66 (b) 69 (c) 198 (d) 22
  19. 19.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 70 (c) 61 (d) 62
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 15 (b) 13 (c) 14 (d) 4
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 2 (b) 3 (c) 1 (d) 4
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 87? (a) 19 (b) 20 (c) 8 (d) 18
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 9 (b) 6 (c) 8 (d) 7
  24. 24.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) 45 (d) 135
  25. 25.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  26. 26.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 220 (c) 223 (d) 213
  27. 27.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  28. 28.The numbers 5 to 13 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) 27 (c) 9 (d) 81
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 7 (d) 18
  30. 30.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) 45 (c) 18 (d) 5
  31. 31.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 7 (d) 6
  32. 32.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 166 (c) 148 (d) 158
  33. 33.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
  34. 34.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) 23 (c) 72 (d) 69
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 5 (b) 14 (c) 15 (d) 16
  36. 36.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 529 (b) 424 (c) 519 (d) 528
  37. 37.How many times is the digit 7 written when you write all the numbers from 1 to 74? (a) 10 (b) 7 (c) 13 (d) 12
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 87? (a) 9 (b) 6 (c) 8 (d) 7
  39. 39.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 2 (b) 5 (c) 3 (d) 4

Answer key

  1. 489
  2. 7
  3. 2
  4. 75
  5. 17
  6. 606
  7. 12
  8. 7
  9. 15
  10. 192
  11. 5
  12. 4
  13. 57
  14. 54
  15. 37
  16. 72
  17. 30
  18. 66
  19. 61
  20. 14
  21. 3
  22. 19
  23. 8
  24. 45
  25. 7
  26. 222
  27. 8
  28. 27
  29. 18
  30. 15
  31. 6
  32. 157
  33. 42
  34. 69
  35. 15
  36. 528
  37. 12
  38. 8
  39. 5
  40. 4

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