← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 291 · 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 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) 24 (c) 63 (d) 7
  2. 2.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) 33 (b) 99 (c) 11 (d) 36
  3. 3.The numbers 9 to 17 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) 39 (c) 117 (d) 13
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 2 (b) 5 (c) 4 (d) 3
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 1 (b) 4 (c) 3 (d) 2
  6. 6.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 2 (d) 3
  7. 7.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 396 (b) 342 (c) 406 (d) 405
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 65? (a) 12 (b) 10 (c) 6 (d) 13
  9. 9.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 435 (b) 444 (c) 368 (d) 445
  10. 10.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 145 (b) 154 (c) 146 (d) 136
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 16 (b) 15 (c) 17 (d) 5
  13. 13.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) 207 (c) 72 (d) 69
  14. 14.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 160 (b) 159 (c) 168 (d) 150
  15. 15.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
  16. 16.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
  17. 17.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 7 (c) 6 (d) 13
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 74? (a) 19 (b) 18 (c) 17 (d) 7
  19. 19.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 456 (c) 466 (d) 465
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 12 (b) 13 (c) 3 (d) 14
  21. 21.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 135 (b) 144 (c) 136 (d) 126
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 93? (a) 20 (b) 21 (c) 9 (d) 19
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 15 (b) 17 (c) 16 (d) 5
  24. 24.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 58 (c) 66 (d) 57
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 5 (b) 4 (c) 2 (d) 3
  26. 26.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) 14 (c) 45 (d) 126
  27. 27.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) 5 (b) 18 (c) 45 (d) 15
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 9 (d) 21
  29. 29.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 486 (c) 612 (d) 622
  30. 30.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 3 (d) 10
  31. 31.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) 27 (b) 30 (c) 81 (d) 9
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 1 (b) 3 (c) 2 (d) 4
  33. 33.A book has 35 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 70 (c) 52 (d) 61
  34. 34.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 26 (c) 36 (d) 35
  35. 35.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 507 (c) 508 (d) 498
  36. 36.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 226 (b) 222 (c) 216 (d) 225
  37. 37.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 169 (b) 178 (c) 160 (d) 170
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 12 (b) 13 (c) 5 (d) 11
  39. 39.A book has 185 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 438 (c) 448 (d) 370
  40. 40.A book has 64 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 110 (c) 128 (d) 119

Answer key

  1. 21
  2. 33
  3. 39
  4. 4
  5. 3
  6. 3
  7. 405
  8. 12
  9. 444
  10. 145
  11. 4
  12. 16
  13. 69
  14. 159
  15. 2
  16. 45
  17. 7
  18. 18
  19. 465
  20. 13
  21. 135
  22. 20
  23. 16
  24. 57
  25. 4
  26. 42
  27. 15
  28. 20
  29. 621
  30. 2
  31. 27
  32. 3
  33. 61
  34. 35
  35. 507
  36. 225
  37. 169
  38. 12
  39. 447
  40. 119

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