← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 805 · 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 13? (a) 7 (b) 14 (c) 6 (d) 5
  2. 2.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 511 (c) 412 (d) 501
  3. 3.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) 402 (d) 346
  4. 4.How many times is the digit 5 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 19 (d) 9
  5. 5.A book has 191 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 466 (b) 456 (c) 382 (d) 465
  6. 6.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 226 (c) 216 (d) 225
  7. 7.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) 5 (b) 15 (c) 18 (d) 45
  8. 8.A book has 226 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 570 (b) 561 (c) 452 (d) 571
  9. 9.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 499 (b) 489 (c) 404 (d) 498
  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) 20 (b) 63 (c) 180 (d) 60
  11. 11.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) 63 (c) 7 (d) 21
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 19 (d) 18
  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) 30 (b) 90 (c) 33 (d) 10
  14. 14.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 72 (c) 62 (d) 71
  15. 15.The numbers 8 to 16 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 12 (b) 108 (c) 39 (d) 36
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 14 (b) 15 (c) 13 (d) 3
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 50? (a) 6 (b) 5 (c) 4 (d) 3
  18. 18.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 32? (a) 4 (b) 1 (c) 3 (d) 2
  20. 20.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 200 (b) 183 (c) 193 (d) 192
  21. 21.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 5 (b) 3 (c) 4 (d) 2
  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) 72 (c) 24 (d) 216
  23. 23.A book has 82 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 146 (b) 164 (c) 156 (d) 155
  24. 24.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 610 (b) 609 (c) 600 (d) 478
  25. 25.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 39 (c) 48 (d) 40
  26. 26.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 4 (d) 3
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 6 (b) 16 (c) 18 (d) 17
  29. 29.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) 36 (b) 99 (c) 11 (d) 33
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 81? (a) 19 (b) 8 (c) 18 (d) 20
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 2 (b) 5 (c) 4 (d) 3
  32. 32.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 185 (b) 194 (c) 176 (d) 186
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 3 (b) 5 (c) 2 (d) 4
  34. 34.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) 135 (b) 15 (c) 48 (d) 45
  35. 35.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 493 (b) 400 (c) 492 (d) 483
  36. 36.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 4 (d) 17
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 67? (a) 16 (b) 18 (c) 17 (d) 6
  38. 38.A book has 89 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 169 (c) 160 (d) 170
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 19 (b) 18 (c) 17 (d) 8
  40. 40.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 10 (c) 11 (d) 8

Answer key

  1. 6
  2. 510
  3. 411
  4. 20
  5. 465
  6. 225
  7. 15
  8. 570
  9. 498
  10. 60
  11. 21
  12. 19
  13. 30
  14. 71
  15. 36
  16. 14
  17. 5
  18. 9
  19. 3
  20. 192
  21. 4
  22. 72
  23. 155
  24. 609
  25. 39
  26. 5
  27. 4
  28. 17
  29. 33
  30. 19
  31. 4
  32. 185
  33. 4
  34. 45
  35. 492
  36. 3
  37. 17
  38. 169
  39. 18
  40. 9

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