← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 453 · 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 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 402 (b) 340 (c) 403 (d) 393
  2. 2.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 10 (c) 11 (d) 9
  3. 3.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 80 (c) 89 (d) 98
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 5 (d) 4
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 15 (b) 17 (c) 16 (d) 7
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 3 (b) 6 (c) 4 (d) 5
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 10 (d) 6
  8. 8.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 330 (c) 321 (d) 292
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 6 (b) 7 (c) 8 (d) 5
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 4 (b) 3 (c) 5 (d) 6
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 18 (b) 20 (c) 9 (d) 19
  12. 12.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 153 (b) 162 (c) 144 (d) 154
  13. 13.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) 18 (b) 15 (c) 45 (d) 5
  14. 14.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) 33 (b) 10 (c) 30 (d) 90
  15. 15.The numbers 4 to 12 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 8 (b) 24 (c) 27 (d) 72
  16. 16.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 565 (c) 555 (d) 448
  17. 17.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) 36 (b) 12 (c) 39 (d) 108
  18. 18.A book has 171 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 405 (b) 396 (c) 342 (d) 406
  19. 19.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  20. 20.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 7 (d) 14
  21. 21.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  22. 22.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
  23. 23.How many times is the digit 3 written when you write all the numbers from 1 to 61? (a) 15 (b) 6 (c) 16 (d) 17
  24. 24.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 600 (c) 610 (d) 609
  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) 207 (b) 23 (c) 69 (d) 72
  26. 26.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 96 (c) 87 (d) 78
  27. 27.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 38? (a) 4 (b) 2 (c) 5 (d) 3
  29. 29.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) 21 (b) 66 (c) 63 (d) 189
  30. 30.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 4 (b) 2 (c) 3 (d) 1
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 1 (b) 4 (c) 2 (d) 3
  32. 32.A book has 145 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 290 (b) 318 (c) 328 (d) 327
  33. 33.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4
  34. 34.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 595 (c) 594 (d) 585
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 99? (a) 21 (b) 19 (c) 9 (d) 20
  36. 36.How many two-digit numbers have digits that add up to 12? (a) 6 (b) 8 (c) 7 (d) 13
  37. 37.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) 51 (d) 54
  38. 38.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 397 (b) 336 (c) 396 (d) 387
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 20 (d) 21
  40. 40.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4

Answer key

  1. 402
  2. 9
  3. 89
  4. 5
  5. 16
  6. 5
  7. 6
  8. 330
  9. 7
  10. 5
  11. 19
  12. 153
  13. 15
  14. 30
  15. 24
  16. 564
  17. 36
  18. 405
  19. 2
  20. 6
  21. 2
  22. 42
  23. 16
  24. 609
  25. 69
  26. 87
  27. 5
  28. 4
  29. 63
  30. 3
  31. 3
  32. 327
  33. 5
  34. 594
  35. 20
  36. 7
  37. 51
  38. 396
  39. 20
  40. 3

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