← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 930 · 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 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) 11 (b) 99 (c) 36 (d) 33
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 75? (a) 8 (b) 5 (c) 7 (d) 6
  3. 3.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  4. 4.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 54 (c) 53 (d) 62
  5. 5.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) 66 (b) 21 (c) 63 (d) 189
  6. 6.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) 81 (b) 9 (c) 27 (d) 30
  7. 7.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 41 (c) 50 (d) 32
  8. 8.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) 24 (b) 216 (c) 72 (d) 75
  9. 9.A book has 79 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 149 (c) 140 (d) 150
  10. 10.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 10 (c) 6 (d) 7
  11. 11.How many times is the digit 5 written when you write all the numbers from 1 to 81? (a) 18 (b) 8 (c) 19 (d) 17
  12. 12.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) 60 (b) 171 (c) 19 (d) 57
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 32? (a) 2 (b) 3 (c) 4 (d) 1
  14. 14.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 10 (c) 8 (d) 7
  15. 15.A book has 90 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 171 (b) 180 (c) 162 (d) 172
  16. 16.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 17 (c) 2 (d) 3
  17. 17.A book has 116 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 240 (b) 231 (c) 241 (d) 232
  18. 18.A book has 66 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 114 (b) 123 (c) 132 (d) 124
  19. 19.How many two-digit numbers have digits that add up to 8? (a) 8 (b) 10 (c) 9 (d) 7
  20. 20.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 612 (b) 486 (c) 621 (d) 622
  21. 21.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) 18 (b) 15 (c) 5 (d) 45
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 10 (c) 2 (d) 4
  23. 23.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) 7 (b) 63 (c) 21 (d) 24
  24. 24.A book has 20 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 22 (c) 31 (d) 32
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 15 (b) 14 (c) 13 (d) 3
  26. 26.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 537 (b) 436 (c) 547 (d) 546
  27. 27.A book has 73 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 128 (c) 138 (d) 137
  28. 28.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) 63 (b) 20 (c) 180 (d) 60
  29. 29.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  30. 30.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 162 (b) 153 (c) 144 (d) 154
  31. 31.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) 52 (c) 43 (d) 34
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 16 (b) 14 (c) 15 (d) 4
  33. 33.A book has 196 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 480 (b) 481 (c) 392 (d) 471
  34. 34.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) 14 (b) 126 (c) 45 (d) 42
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 67? (a) 8 (b) 7 (c) 5 (d) 6
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 37? (a) 2 (b) 4 (c) 3 (d) 5
  37. 37.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 468 (b) 478 (c) 390 (d) 477
  38. 38.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 74 (c) 56 (d) 65
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 18 (b) 17 (c) 16 (d) 7
  40. 40.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 3 (b) 13 (c) 15 (d) 14

Answer key

  1. 33
  2. 7
  3. 4
  4. 53
  5. 63
  6. 27
  7. 41
  8. 72
  9. 149
  10. 6
  11. 18
  12. 57
  13. 3
  14. 7
  15. 171
  16. 3
  17. 240
  18. 123
  19. 8
  20. 621
  21. 15
  22. 3
  23. 21
  24. 31
  25. 14
  26. 546
  27. 137
  28. 60
  29. 9
  30. 153
  31. 43
  32. 15
  33. 480
  34. 42
  35. 7
  36. 4
  37. 477
  38. 65
  39. 17
  40. 14

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