← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 149 · 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.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) 162 (c) 54 (d) 57
  2. 2.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  3. 3.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) 528 (c) 519 (d) 424
  4. 4.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  5. 5.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 108 (b) 36 (c) 39 (d) 12
  6. 6.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 114 (c) 123 (d) 124
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 9 (b) 12 (c) 10 (d) 13
  8. 8.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 53 (b) 44 (c) 54 (d) 62
  9. 9.How many times is the digit 7 written when you write all the numbers from 1 to 92? (a) 19 (b) 20 (c) 9 (d) 18
  10. 10.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  11. 11.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 448 (b) 370 (c) 447 (d) 438
  12. 12.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 88 (c) 97 (d) 98
  13. 13.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  14. 14.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 66 (c) 56 (d) 65
  15. 15.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) 126 (b) 14 (c) 42 (d) 45
  16. 16.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 119 (b) 110 (c) 128 (d) 120
  17. 17.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 3 (b) 4 (c) 1 (d) 2
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 3 (b) 2 (c) 4 (d) 1
  19. 19.A book has 27 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 54 (b) 45 (c) 46 (d) 36
  20. 20.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 6 (c) 10 (d) 5
  21. 21.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 150 (b) 158 (c) 149 (d) 140
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 2 (b) 3 (c) 4 (d) 5
  23. 23.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) 72 (c) 75 (d) 24
  24. 24.How many times is the digit 3 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 21 (d) 20
  25. 25.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) 72 (c) 207 (d) 69
  26. 26.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 11 (d) 10
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 21 (b) 19 (c) 9 (d) 20
  28. 28.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 202 (c) 201 (d) 192
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 51? (a) 5 (b) 17 (c) 16 (d) 15
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 99? (a) 9 (b) 20 (c) 19 (d) 21
  31. 31.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 168 (c) 177 (d) 186
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 9 (b) 4 (c) 10 (d) 11
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 6 (b) 4 (c) 5 (d) 3
  34. 34.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 282 (b) 266 (c) 292 (d) 291
  35. 35.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) 5 (c) 18 (d) 15
  36. 36.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 7 (b) 6 (c) 8 (d) 9
  37. 37.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) 10 (c) 33 (d) 30
  38. 38.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) 45 (b) 48 (c) 135 (d) 15
  39. 39.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
  40. 40.A book has 128 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 267 (b) 277 (c) 256 (d) 276

Answer key

  1. 54
  2. 7
  3. 528
  4. 2
  5. 36
  6. 123
  7. 12
  8. 53
  9. 19
  10. 3
  11. 447
  12. 97
  13. 2
  14. 65
  15. 42
  16. 119
  17. 3
  18. 3
  19. 45
  20. 6
  21. 149
  22. 4
  23. 72
  24. 20
  25. 69
  26. 9
  27. 20
  28. 201
  29. 16
  30. 20
  31. 177
  32. 10
  33. 5
  34. 291
  35. 15
  36. 8
  37. 30
  38. 45
  39. 63
  40. 276

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