← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 467 · 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 two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  2. 2.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) 66 (b) 189 (c) 21 (d) 63
  3. 3.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 484 (c) 609 (d) 619
  4. 4.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 1 (b) 3 (c) 2 (d) 4
  5. 5.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 7 (b) 8 (c) 9 (d) 6
  6. 6.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  7. 7.A book has 136 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 300 (b) 301 (c) 291 (d) 272
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 1 (d) 2
  9. 9.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 5 (d) 2
  12. 12.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 3 (d) 4
  13. 13.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
  14. 14.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) 69 (c) 72 (d) 23
  15. 15.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 99? (a) 21 (b) 20 (c) 9 (d) 19
  17. 17.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 10 (c) 2 (d) 3
  18. 18.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 198 (b) 66 (c) 22 (d) 69
  19. 19.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) 72 (b) 27 (c) 24 (d) 8
  20. 20.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) 51 (c) 144 (d) 48
  21. 21.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 10 (c) 8 (d) 9
  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) 14 (b) 126 (c) 45 (d) 42
  23. 23.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 162 (c) 161 (d) 170
  24. 24.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) 9 (b) 30 (c) 27 (d) 81
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 37? (a) 3 (b) 12 (c) 13 (d) 11
  26. 26.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  27. 27.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) 18 (c) 54 (d) 21
  28. 28.A book has 120 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 253 (b) 243 (c) 252 (d) 240
  29. 29.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 124 (b) 123 (c) 132 (d) 114
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 14 (b) 15 (c) 3 (d) 13
  31. 31.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 68 (c) 77 (d) 78
  32. 32.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) 153 (b) 17 (c) 54 (d) 51
  33. 33.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 424 (b) 414 (c) 423 (d) 354
  34. 34.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) 556 (c) 546 (d) 442
  35. 35.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 478 (c) 390 (d) 477
  36. 36.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 43? (a) 4 (b) 8 (c) 9 (d) 6
  38. 38.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 6 (c) 7 (d) 8
  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) 39 (b) 117 (c) 42 (d) 13
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 49? (a) 16 (b) 4 (c) 15 (d) 14

Answer key

  1. 9
  2. 63
  3. 618
  4. 3
  5. 8
  6. 4
  7. 300
  8. 3
  9. 6
  10. 7
  11. 4
  12. 4
  13. 51
  14. 69
  15. 2
  16. 20
  17. 3
  18. 66
  19. 24
  20. 48
  21. 8
  22. 42
  23. 161
  24. 27
  25. 12
  26. 5
  27. 18
  28. 252
  29. 123
  30. 14
  31. 77
  32. 51
  33. 423
  34. 555
  35. 477
  36. 9
  37. 8
  38. 7
  39. 39
  40. 15

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