← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 397 · 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 11? (a) 9 (b) 12 (c) 8 (d) 7
  2. 2.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) 72 (b) 23 (c) 207 (d) 69
  3. 3.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  4. 4.A book has 46 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 74 (b) 84 (c) 92 (d) 83
  5. 5.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) 42 (b) 13 (c) 39 (d) 117
  6. 6.How many times is the digit 5 written when you write all the numbers from 1 to 33? (a) 1 (b) 2 (c) 3 (d) 4
  7. 7.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) 21 (c) 7 (d) 24
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 5 (b) 6 (c) 4 (d) 3
  9. 9.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) 30 (b) 33 (c) 90 (d) 10
  10. 10.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) 20 (d) 63
  11. 11.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) 54 (c) 21 (d) 6
  12. 12.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 52 (b) 34 (c) 44 (d) 43
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 86? (a) 8 (b) 9 (c) 6 (d) 7
  14. 14.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 46? (a) 15 (b) 16 (c) 14 (d) 4
  16. 16.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  17. 17.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 174 (c) 156 (d) 165
  18. 18.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 488 (c) 625 (d) 624
  19. 19.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 70 (c) 79 (d) 80
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 16 (d) 4
  21. 21.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 3 (c) 2 (d) 17
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 20 (d) 9
  23. 23.A book has 62 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 116 (c) 115 (d) 124
  24. 24.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 517 (c) 516 (d) 416
  25. 25.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 47 (c) 48 (d) 38
  26. 26.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 5 (b) 4 (c) 7 (d) 6
  27. 27.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) 21 (b) 189 (c) 66 (d) 63
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 9 (b) 20 (c) 18 (d) 19
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 16 (b) 4 (c) 15 (d) 14
  30. 30.A book has 169 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 338 (c) 400 (d) 399
  31. 31.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 144 (c) 162 (d) 153
  32. 32.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) 42 (b) 14 (c) 45 (d) 126
  33. 33.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 242 (b) 256 (c) 246 (d) 255
  34. 34.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 6 (c) 5 (d) 4
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 3 (b) 14 (c) 15 (d) 13
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 9 (d) 19
  37. 37.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  38. 38.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 14 (c) 6 (d) 7
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 3 (b) 2 (c) 5 (d) 4
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 90? (a) 20 (b) 18 (c) 9 (d) 19

Answer key

  1. 8
  2. 69
  3. 9
  4. 83
  5. 39
  6. 3
  7. 21
  8. 5
  9. 30
  10. 60
  11. 18
  12. 43
  13. 8
  14. 3
  15. 15
  16. 5
  17. 165
  18. 624
  19. 79
  20. 4
  21. 3
  22. 20
  23. 115
  24. 516
  25. 47
  26. 6
  27. 63
  28. 19
  29. 15
  30. 399
  31. 153
  32. 42
  33. 255
  34. 5
  35. 14
  36. 20
  37. 4
  38. 6
  39. 4
  40. 19

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