← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 67 · 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 14? (a) 15 (b) 5 (c) 6 (d) 4
  2. 2.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 20 (b) 8 (c) 19 (d) 18
  3. 3.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) 33 (c) 10 (d) 30
  4. 4.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) 24 (b) 7 (c) 63 (d) 21
  5. 5.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 185 (c) 176 (d) 194
  6. 6.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 6 (b) 5 (c) 4 (d) 7
  8. 8.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 4 (d) 3
  9. 9.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 411 (c) 346 (d) 402
  10. 10.The numbers 11 to 19 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) 48 (c) 45 (d) 135
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 7 (d) 18
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 51? (a) 3 (b) 6 (c) 4 (d) 5
  13. 13.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  14. 14.A book has 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 470 (b) 588 (c) 597 (d) 598
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 63? (a) 6 (b) 10 (c) 11 (d) 8
  16. 16.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 10 (c) 8 (d) 11
  17. 17.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 90 (c) 80 (d) 98
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 16 (b) 15 (c) 6 (d) 17
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 16 (b) 15 (c) 14 (d) 4
  20. 20.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) 21 (b) 6 (c) 54 (d) 18
  21. 21.How many times is the digit 3 written when you write all the numbers from 1 to 45? (a) 4 (b) 16 (c) 14 (d) 15
  22. 22.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) 75 (b) 24 (c) 72 (d) 216
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 3 (b) 5 (c) 6 (d) 4
  24. 24.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 9 (c) 10 (d) 11
  25. 25.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) 24 (c) 27 (d) 8
  26. 26.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 7 (d) 9
  27. 27.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 6 (b) 16 (c) 18 (d) 17
  28. 28.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  29. 29.A book has 250 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 633 (b) 642 (c) 643 (d) 500
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 18 (b) 7 (c) 19 (d) 17
  31. 31.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 196 (c) 187 (d) 188
  32. 32.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) 69 (b) 22 (c) 66 (d) 198
  33. 33.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 83 (b) 74 (c) 84 (d) 92
  34. 34.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) 60 (b) 63 (c) 20 (d) 180
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 9 (b) 7 (c) 10 (d) 5
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 4 (d) 16
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 2 (d) 3
  38. 38.The numbers 14 to 22 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) 57 (c) 162 (d) 54
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 20 (b) 18 (c) 8 (d) 19
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 18 (b) 19 (c) 17 (d) 8

Answer key

  1. 5
  2. 19
  3. 30
  4. 21
  5. 185
  6. 4
  7. 6
  8. 3
  9. 411
  10. 45
  11. 18
  12. 5
  13. 5
  14. 597
  15. 10
  16. 9
  17. 89
  18. 16
  19. 15
  20. 18
  21. 15
  22. 72
  23. 5
  24. 9
  25. 24
  26. 8
  27. 17
  28. 6
  29. 642
  30. 18
  31. 187
  32. 66
  33. 83
  34. 60
  35. 9
  36. 15
  37. 3
  38. 54
  39. 19
  40. 18

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