← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 632 · 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.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) 63 (b) 21 (c) 189 (d) 66
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 19 (d) 9
  3. 3.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 58 (c) 57 (d) 66
  4. 4.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 66 (c) 75 (d) 84
  5. 5.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 8 (c) 9 (d) 10
  6. 6.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 19 (b) 18 (c) 7 (d) 17
  8. 8.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) 5 (d) 15
  9. 9.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 8 (d) 7
  11. 11.How many times is the digit 7 written when you write all the numbers from 1 to 75? (a) 13 (b) 14 (c) 7 (d) 11
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 4 (d) 3
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 97? (a) 9 (b) 19 (c) 18 (d) 20
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 2 (d) 1
  15. 15.A book has 61 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 113 (b) 122 (c) 114 (d) 104
  16. 16.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) 180 (c) 63 (d) 20
  17. 17.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 12 (d) 9
  18. 18.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) 21 (d) 24
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 2 (b) 5 (c) 4 (d) 3
  20. 20.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 9 (c) 7 (d) 10
  21. 21.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  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) 216 (b) 75 (c) 72 (d) 24
  23. 23.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 74 (c) 83 (d) 92
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 16 (b) 17 (c) 8 (d) 14
  25. 25.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 3 (b) 6 (c) 5 (d) 4
  27. 27.How many times is the digit 7 written when you write all the numbers from 1 to 40? (a) 4 (b) 2 (c) 5 (d) 3
  28. 28.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 543 (b) 553 (c) 440 (d) 552
  29. 29.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) 48 (b) 16 (c) 144 (d) 51
  30. 30.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  31. 31.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) 23 (b) 69 (c) 207 (d) 72
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 20 (b) 19 (c) 9 (d) 21
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 92? (a) 9 (b) 19 (c) 20 (d) 18
  34. 34.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 162 (c) 172 (d) 171
  35. 35.A book has 186 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 441 (b) 372 (c) 451 (d) 450
  36. 36.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) 21 (c) 18 (d) 54
  37. 37.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 416 (c) 507 (d) 517
  38. 38.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 498 (c) 508 (d) 507
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 13 (d) 6
  40. 40.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) 57 (b) 18 (c) 54 (d) 162

Answer key

  1. 63
  2. 20
  3. 57
  4. 75
  5. 9
  6. 4
  7. 18
  8. 15
  9. 5
  10. 7
  11. 13
  12. 3
  13. 19
  14. 3
  15. 113
  16. 60
  17. 8
  18. 21
  19. 4
  20. 8
  21. 3
  22. 72
  23. 83
  24. 16
  25. 6
  26. 5
  27. 4
  28. 552
  29. 48
  30. 9
  31. 69
  32. 20
  33. 19
  34. 171
  35. 450
  36. 18
  37. 516
  38. 507
  39. 7
  40. 54

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