← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 688 · 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 7? (a) 6 (b) 8 (c) 10 (d) 7
  2. 2.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) 30 (c) 90 (d) 10
  3. 3.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 19 (b) 21 (c) 20 (d) 9
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 3 (b) 4 (c) 5 (d) 6
  5. 5.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) 15 (b) 5 (c) 18 (d) 45
  6. 6.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) 13 (b) 42 (c) 117 (d) 39
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 79? (a) 17 (b) 18 (c) 19 (d) 7
  8. 8.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 14 (b) 11 (c) 8 (d) 13
  9. 9.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 10 (d) 9
  10. 10.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 8 (d) 9
  11. 11.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) 12 (b) 108 (c) 39 (d) 36
  12. 12.The numbers 7 to 15 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) 11 (c) 99 (d) 33
  13. 13.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 238 (c) 240 (d) 249
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 57? (a) 5 (b) 6 (c) 7 (d) 4
  15. 15.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 18 (b) 6 (c) 16 (d) 17
  16. 16.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) 54 (b) 6 (c) 18 (d) 21
  17. 17.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 585 (b) 594 (c) 595 (d) 468
  18. 18.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 337 (c) 296 (d) 327
  19. 19.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 570 (c) 580 (d) 579
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 65? (a) 7 (b) 6 (c) 5 (d) 4
  21. 21.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  23. 23.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) 63 (c) 60 (d) 20
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 72? (a) 7 (b) 18 (c) 16 (d) 17
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 8 (b) 20 (c) 18 (d) 19
  27. 27.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) 81 (d) 27
  28. 28.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  29. 29.A book has 68 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 127 (b) 136 (c) 118 (d) 128
  30. 30.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 10 (d) 7
  31. 31.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 17 (b) 6 (c) 16 (d) 15
  32. 32.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 9 (d) 20
  33. 33.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 3 (b) 5 (c) 4 (d) 6
  34. 34.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) 222 (c) 226 (d) 231
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 13 (b) 12 (c) 14 (d) 3
  36. 36.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) 72 (b) 216 (c) 24 (d) 75
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 4 (b) 16 (c) 14 (d) 15
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 5 (b) 8 (c) 7 (d) 4
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 69? (a) 6 (b) 8 (c) 5 (d) 7
  40. 40.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2

Answer key

  1. 7
  2. 30
  3. 20
  4. 5
  5. 15
  6. 39
  7. 18
  8. 13
  9. 9
  10. 9
  11. 36
  12. 33
  13. 249
  14. 6
  15. 17
  16. 18
  17. 594
  18. 336
  19. 579
  20. 6
  21. 4
  22. 3
  23. 60
  24. 4
  25. 17
  26. 19
  27. 27
  28. 2
  29. 127
  30. 8
  31. 16
  32. 20
  33. 5
  34. 231
  35. 13
  36. 72
  37. 15
  38. 7
  39. 7
  40. 3

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