← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 414 · 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 times is the digit 1 written when you write all the numbers from 1 to 78? (a) 17 (b) 7 (c) 19 (d) 18
  2. 2.How many times is the digit 5 written when you write all the numbers from 1 to 41? (a) 4 (b) 3 (c) 2 (d) 5
  3. 3.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 6 (b) 3 (c) 5 (d) 4
  4. 4.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 3 (c) 4 (d) 5
  5. 5.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  6. 6.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) 108 (c) 39 (d) 12
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 84? (a) 7 (b) 6 (c) 8 (d) 9
  8. 8.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 4 (d) 5
  9. 9.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 6 (b) 5 (c) 7 (d) 8
  11. 11.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 16 (b) 15 (c) 17 (d) 5
  12. 12.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 79 (c) 88 (d) 70
  13. 13.A book has 166 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 332 (b) 381 (c) 391 (d) 390
  14. 14.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) 98 (d) 89
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 17 (b) 6 (c) 18 (d) 16
  16. 16.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 504 (b) 505 (c) 495 (d) 408
  17. 17.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  18. 18.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 228 (c) 225 (d) 235
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 91? (a) 18 (b) 20 (c) 9 (d) 19
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 50? (a) 14 (b) 15 (c) 5 (d) 16
  21. 21.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  22. 22.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 18 (c) 1 (d) 2
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  24. 24.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  25. 25.The numbers 16 to 24 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 180 (b) 20 (c) 63 (d) 60
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 4 (b) 5 (c) 2 (d) 3
  27. 27.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 90 (c) 72 (d) 81
  28. 28.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 166 (c) 158 (d) 157
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 15 (b) 4 (c) 14 (d) 16
  30. 30.A book has 113 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 232 (b) 231 (c) 222 (d) 226
  31. 31.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  32. 32.A book has 183 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 432 (b) 366 (c) 442 (d) 441
  33. 33.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) 39 (b) 42 (c) 13 (d) 117
  34. 34.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 160 (c) 150 (d) 159
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 75? (a) 16 (b) 18 (c) 7 (d) 17
  36. 36.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) 76 (c) 94 (d) 85
  37. 37.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 488 (c) 625 (d) 624
  38. 38.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 480 (c) 613 (d) 612
  39. 39.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 105 (c) 114 (d) 106
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 89? (a) 8 (b) 18 (c) 19 (d) 20

Answer key

  1. 18
  2. 4
  3. 5
  4. 4
  5. 3
  6. 36
  7. 8
  8. 5
  9. 5
  10. 7
  11. 16
  12. 79
  13. 390
  14. 89
  15. 17
  16. 504
  17. 8
  18. 234
  19. 19
  20. 15
  21. 4
  22. 2
  23. 8
  24. 7
  25. 60
  26. 4
  27. 81
  28. 157
  29. 15
  30. 231
  31. 9
  32. 441
  33. 39
  34. 159
  35. 17
  36. 85
  37. 624
  38. 612
  39. 105
  40. 19

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