← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 225 · 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) 8 (b) 7 (c) 9 (d) 12
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 9 (b) 10 (c) 11 (d) 3
  3. 3.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 549 (b) 558 (c) 559 (d) 444
  4. 4.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) 60 (c) 78 (d) 69
  5. 5.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 520 (c) 418 (d) 519
  6. 6.A book has 87 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 174 (b) 165 (c) 166 (d) 156
  7. 7.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) 15 (b) 135 (c) 45 (d) 48
  8. 8.A book has 248 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 627 (b) 637 (c) 496 (d) 636
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 20 (d) 21
  10. 10.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) 24 (d) 21
  11. 11.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8
  12. 12.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
  13. 13.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 8 (c) 10 (d) 7
  14. 14.A book has 239 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 610 (c) 600 (d) 609
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 77? (a) 18 (b) 7 (c) 19 (d) 17
  16. 16.A book has 164 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 328 (b) 375 (c) 385 (d) 384
  17. 17.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) 144 (c) 16 (d) 51
  18. 18.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 14 (b) 16 (c) 15 (d) 4
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 73? (a) 19 (b) 18 (c) 7 (d) 17
  20. 20.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
  21. 21.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 102 (b) 84 (c) 94 (d) 93
  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) 72 (b) 24 (c) 216 (d) 75
  23. 23.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) 39 (c) 117 (d) 13
  24. 24.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) 57 (b) 171 (c) 60 (d) 19
  25. 25.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 17 (b) 18 (c) 19 (d) 8
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 83? (a) 20 (b) 18 (c) 8 (d) 19
  27. 27.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 5 (c) 4 (d) 15
  28. 28.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 10 (d) 4
  29. 29.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) 15 (d) 5
  30. 30.A book has 228 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 567 (c) 576 (d) 577
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 16 (b) 5 (c) 17 (d) 15
  32. 32.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 511 (b) 510 (c) 412 (d) 501
  33. 33.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  34. 34.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) 33 (b) 10 (c) 30 (d) 90
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 20 (b) 18 (c) 19 (d) 9
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 20 (b) 8 (c) 18 (d) 19
  37. 37.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 616 (b) 615 (c) 606 (d) 482
  38. 38.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 89 (c) 90 (d) 98
  39. 39.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) 72 (b) 27 (c) 24 (d) 8
  40. 40.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 295 (c) 268 (d) 285

Answer key

  1. 8
  2. 10
  3. 558
  4. 69
  5. 519
  6. 165
  7. 45
  8. 636
  9. 20
  10. 21
  11. 9
  12. 60
  13. 7
  14. 609
  15. 18
  16. 384
  17. 48
  18. 15
  19. 18
  20. 27
  21. 93
  22. 72
  23. 39
  24. 57
  25. 18
  26. 19
  27. 5
  28. 4
  29. 15
  30. 576
  31. 16
  32. 510
  33. 5
  34. 30
  35. 19
  36. 19
  37. 615
  38. 89
  39. 24
  40. 294

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