← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 802 · 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.A book has 121 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 256 (b) 242 (c) 255 (d) 246
  2. 2.A book has 220 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 553 (b) 440 (c) 552 (d) 543
  3. 3.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 112 (c) 111 (d) 102
  4. 4.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) 180 (b) 60 (c) 63 (d) 20
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 5 (b) 7 (c) 8 (d) 6
  6. 6.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) 66 (c) 21 (d) 63
  7. 7.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 6 (d) 8
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 15 (b) 16 (c) 14 (d) 4
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 93? (a) 20 (b) 19 (c) 18 (d) 9
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 49? (a) 16 (b) 14 (c) 4 (d) 15
  12. 12.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  13. 13.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) 10 (b) 33 (c) 30 (d) 90
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 15 (d) 4
  15. 15.A book has 96 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 174 (c) 183 (d) 184
  16. 16.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) 13 (b) 117 (c) 39 (d) 42
  17. 17.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) 18 (c) 54 (d) 6
  18. 18.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) 48 (b) 135 (c) 45 (d) 15
  19. 19.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 8 (d) 6
  20. 20.A book has 211 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 516 (b) 526 (c) 525 (d) 422
  21. 21.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 6 (b) 3 (c) 5 (d) 4
  22. 22.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  23. 23.How many times is the digit 7 written when you write all the numbers from 1 to 54? (a) 6 (b) 3 (c) 5 (d) 4
  24. 24.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  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) 27 (b) 8 (c) 24 (d) 72
  26. 26.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) 15 (b) 5 (c) 45 (d) 18
  27. 27.A book has 238 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 607 (b) 597 (c) 476 (d) 606
  28. 28.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
  29. 29.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  30. 30.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 9 (c) 12 (d) 7
  31. 31.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 58 (b) 50 (c) 40 (d) 49
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 19 (b) 21 (c) 20 (d) 9
  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) 30 (b) 27 (c) 9 (d) 81
  34. 34.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 69 (c) 78 (d) 60
  35. 35.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) 188 (c) 196 (d) 187
  36. 36.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) 144 (c) 153 (d) 154
  37. 37.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 166 (c) 175 (d) 184
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 3 (d) 4
  39. 39.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 136 (c) 126 (d) 135
  40. 40.How many times is the digit 8 written when you write all the numbers from 1 to 87? (a) 17 (b) 8 (c) 14 (d) 16

Answer key

  1. 255
  2. 552
  3. 111
  4. 60
  5. 7
  6. 63
  7. 7
  8. 15
  9. 4
  10. 19
  11. 15
  12. 6
  13. 30
  14. 5
  15. 183
  16. 39
  17. 18
  18. 45
  19. 7
  20. 525
  21. 5
  22. 5
  23. 5
  24. 3
  25. 24
  26. 15
  27. 606
  28. 2
  29. 3
  30. 8
  31. 49
  32. 20
  33. 27
  34. 69
  35. 187
  36. 153
  37. 175
  38. 3
  39. 135
  40. 16

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