← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 531 · 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 46? (a) 14 (b) 16 (c) 4 (d) 15
  2. 2.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
  3. 3.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) 144 (b) 51 (c) 16 (d) 48
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 15 (b) 16 (c) 4 (d) 14
  5. 5.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 17 (c) 4 (d) 2
  6. 6.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 262 (b) 252 (c) 246 (d) 261
  7. 7.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 10 (d) 1
  8. 8.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 462 (b) 576 (c) 585 (d) 586
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 99? (a) 19 (b) 20 (c) 9 (d) 21
  10. 10.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
  11. 11.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 5 (d) 6
  12. 12.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) 108 (b) 12 (c) 39 (d) 36
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 19 (d) 9
  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) 72 (c) 27 (d) 24
  16. 16.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 338 (c) 400 (d) 390
  17. 17.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 43 (c) 52 (d) 34
  18. 18.The numbers 15 to 23 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 171 (b) 19 (c) 57 (d) 60
  19. 19.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 9 (b) 19 (c) 21 (d) 20
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  21. 21.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) 90 (b) 30 (c) 10 (d) 33
  22. 22.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 84 (c) 74 (d) 83
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
  24. 24.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 11 (c) 9 (d) 10
  25. 25.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  26. 26.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 640 (b) 498 (c) 639 (d) 630
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 14 (b) 15 (c) 4 (d) 16
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 42? (a) 4 (b) 3 (c) 2 (d) 5
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 12 (c) 9 (d) 7
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 4 (b) 2 (c) 1 (d) 3
  31. 31.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) 45 (b) 18 (c) 15 (d) 5
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 17 (b) 18 (c) 8 (d) 19
  33. 33.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) 81 (c) 30 (d) 27
  34. 34.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 32 (b) 41 (c) 42 (d) 50
  35. 35.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 8 (d) 18
  36. 36.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) 63 (b) 7 (c) 24 (d) 21
  37. 37.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 8 (c) 6 (d) 7
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 34? (a) 3 (b) 1 (c) 4 (d) 2
  39. 39.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) 18 (b) 6 (c) 21 (d) 54
  40. 40.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 228 (b) 237 (c) 238 (d) 230

Answer key

  1. 15
  2. 42
  3. 48
  4. 15
  5. 3
  6. 261
  7. 2
  8. 585
  9. 20
  10. 63
  11. 6
  12. 36
  13. 8
  14. 20
  15. 24
  16. 399
  17. 43
  18. 57
  19. 20
  20. 7
  21. 30
  22. 83
  23. 3
  24. 9
  25. 4
  26. 639
  27. 15
  28. 4
  29. 8
  30. 3
  31. 15
  32. 18
  33. 27
  34. 41
  35. 19
  36. 21
  37. 7
  38. 3
  39. 18
  40. 237

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