← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 749 · 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 12 to 20 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 48 (b) 144 (c) 51 (d) 16
  2. 2.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 226 (c) 222 (d) 225
  3. 3.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 446 (c) 561 (d) 552
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 8 (d) 7
  5. 5.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) 45 (c) 14 (d) 42
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 16 (c) 6 (d) 17
  7. 7.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 113 (c) 122 (d) 104
  8. 8.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 441 (c) 442 (d) 432
  9. 9.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 457 (c) 447 (d) 456
  10. 10.How many times is the digit 3 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 17 (d) 16
  11. 11.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) 17 (b) 153 (c) 54 (d) 51
  12. 12.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 194 (c) 185 (d) 176
  13. 13.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) 6 (b) 21 (c) 18 (d) 54
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 96? (a) 16 (b) 14 (c) 17 (d) 9
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 5 (b) 4 (c) 6 (d) 7
  16. 16.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 100 (b) 99 (c) 108 (d) 90
  17. 17.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) 7 (b) 21 (c) 24 (d) 63
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 10 (d) 9
  19. 19.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 64? (a) 7 (b) 4 (c) 6 (d) 5
  21. 21.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
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  23. 23.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 90 (c) 89 (d) 80
  24. 24.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 86 (c) 95 (d) 104
  25. 25.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 4 (d) 5
  26. 26.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  27. 27.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) 57 (b) 19 (c) 60 (d) 171
  28. 28.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 7 (d) 9
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 16 (b) 17 (c) 18 (d) 7
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 15 (b) 16 (c) 14 (d) 5
  31. 31.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) 24 (c) 72 (d) 75
  32. 32.A book has 157 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 314 (c) 363 (d) 354
  33. 33.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 384 (b) 334 (c) 394 (d) 393
  34. 34.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) 62 (d) 61
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 8 (b) 18 (c) 19 (d) 17
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 40? (a) 3 (b) 6 (c) 4 (d) 5
  37. 37.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 7 (d) 6
  38. 38.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 520 (b) 519 (c) 418 (d) 510
  39. 39.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) 13 (d) 117
  40. 40.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 402 (c) 412 (d) 411

Answer key

  1. 48
  2. 225
  3. 561
  4. 7
  5. 42
  6. 17
  7. 113
  8. 441
  9. 456
  10. 17
  11. 51
  12. 185
  13. 18
  14. 16
  15. 6
  16. 99
  17. 21
  18. 9
  19. 5
  20. 6
  21. 36
  22. 3
  23. 89
  24. 95
  25. 5
  26. 8
  27. 57
  28. 8
  29. 17
  30. 15
  31. 72
  32. 363
  33. 393
  34. 61
  35. 18
  36. 5
  37. 7
  38. 519
  39. 39
  40. 411

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