← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 112 · 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 two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 13 (d) 8
  2. 2.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 367 (b) 366 (c) 357 (d) 316
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 94? (a) 18 (b) 20 (c) 19 (d) 9
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 16 (b) 17 (c) 6 (d) 18
  5. 5.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 9 (c) 11 (d) 8
  6. 6.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
  7. 7.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 460 (c) 459 (d) 450
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 9 (b) 20 (c) 19 (d) 18
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 3 (d) 2
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 19 (d) 9
  11. 11.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
  12. 12.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 10 (c) 8 (d) 7
  13. 13.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) 39 (c) 36 (d) 12
  14. 14.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) 75 (b) 216 (c) 72 (d) 24
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 17 (b) 7 (c) 19 (d) 18
  16. 16.How many times is the digit 2 written when you write all the numbers from 1 to 94? (a) 21 (b) 20 (c) 9 (d) 19
  17. 17.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 132 (b) 122 (c) 140 (d) 131
  18. 18.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 152 (c) 143 (d) 144
  19. 19.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 15 (b) 13 (c) 14 (d) 3
  21. 21.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) 69 (b) 72 (c) 207 (d) 23
  22. 22.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  23. 23.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) 21 (b) 7 (c) 24 (d) 63
  24. 24.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 8 (c) 9 (d) 12
  25. 25.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) 66 (d) 21
  26. 26.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 252 (b) 240 (c) 253 (d) 243
  27. 27.How many times is the digit 3 written when you write all the numbers from 1 to 97? (a) 19 (b) 9 (c) 21 (d) 20
  28. 28.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 94 (c) 85 (d) 76
  29. 29.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 18 (b) 8 (c) 17 (d) 19
  30. 30.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 6 (d) 5
  31. 31.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  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) 158 (b) 166 (c) 157 (d) 148
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 4 (b) 5 (c) 3 (d) 2
  34. 34.A book has 86 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 164 (c) 163 (d) 172
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 8 (b) 18 (c) 19 (d) 20
  36. 36.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  37. 37.How many times is the digit 6 written when you write all the numbers from 1 to 69? (a) 17 (b) 16 (c) 6 (d) 18
  38. 38.A book has 143 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 322 (b) 286 (c) 321 (d) 312
  39. 39.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 142 (b) 124 (c) 134 (d) 133
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 2 (b) 3 (c) 4 (d) 5

Answer key

  1. 7
  2. 366
  3. 19
  4. 17
  5. 9
  6. 18
  7. 459
  8. 19
  9. 3
  10. 20
  11. 18
  12. 8
  13. 36
  14. 72
  15. 18
  16. 20
  17. 131
  18. 143
  19. 2
  20. 14
  21. 69
  22. 4
  23. 21
  24. 8
  25. 63
  26. 252
  27. 20
  28. 85
  29. 18
  30. 5
  31. 3
  32. 157
  33. 4
  34. 163
  35. 19
  36. 9
  37. 17
  38. 321
  39. 133
  40. 4

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