← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 668 · 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 3 written when you write all the numbers from 1 to 34? (a) 9 (b) 10 (c) 8 (d) 3
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 73? (a) 16 (b) 18 (c) 17 (d) 7
  3. 3.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 70? (a) 7 (b) 6 (c) 8 (d) 9
  5. 5.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 76 (c) 66 (d) 75
  6. 6.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) 42 (c) 45 (d) 14
  7. 7.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) 21 (c) 66 (d) 63
  8. 8.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 7 (c) 14 (d) 5
  9. 9.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  10. 10.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) 63 (c) 21 (d) 24
  11. 11.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 52 (c) 60 (d) 51
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 53? (a) 15 (b) 17 (c) 5 (d) 16
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 79? (a) 18 (b) 7 (c) 19 (d) 17
  14. 14.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  15. 15.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) 16 (b) 144 (c) 48 (d) 51
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  17. 17.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 397 (c) 336 (d) 396
  18. 18.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 10 (d) 9
  19. 19.How many times is the digit 7 written when you write all the numbers from 1 to 91? (a) 9 (b) 19 (c) 20 (d) 18
  20. 20.A book has 221 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 555 (b) 546 (c) 442 (d) 556
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 82? (a) 17 (b) 19 (c) 18 (d) 8
  22. 22.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  23. 23.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) 72 (c) 69 (d) 23
  24. 24.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  25. 25.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 90 (c) 82 (d) 81
  26. 26.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 5 (b) 2 (c) 3 (d) 4
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 66? (a) 7 (b) 6 (c) 4 (d) 5
  29. 29.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 107 (c) 108 (d) 116
  30. 30.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 100 (c) 99 (d) 90
  31. 31.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) 39 (b) 36 (c) 108 (d) 12
  32. 32.A book has 216 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 531 (b) 540 (c) 541 (d) 432
  33. 33.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 115 (c) 124 (d) 116
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 8 (b) 18 (c) 17 (d) 19
  35. 35.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 216 (c) 207 (d) 217
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 19 (b) 20 (c) 18 (d) 8
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 2 (b) 5 (c) 4 (d) 3
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 6 (b) 5 (c) 7 (d) 8
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 5 (b) 13 (c) 12 (d) 14
  40. 40.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 6 (c) 7 (d) 5

Answer key

  1. 9
  2. 17
  3. 5
  4. 8
  5. 75
  6. 42
  7. 63
  8. 6
  9. 8
  10. 21
  11. 51
  12. 16
  13. 18
  14. 7
  15. 48
  16. 2
  17. 396
  18. 8
  19. 19
  20. 555
  21. 18
  22. 2
  23. 69
  24. 3
  25. 81
  26. 4
  27. 4
  28. 6
  29. 107
  30. 99
  31. 36
  32. 540
  33. 115
  34. 18
  35. 216
  36. 19
  37. 4
  38. 7
  39. 13
  40. 6

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