← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 571 · 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 times is the digit 8 written when you write all the numbers from 1 to 92? (a) 18 (b) 9 (c) 20 (d) 19
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 1 (b) 3 (c) 4 (d) 2
  3. 3.The numbers 14 to 22 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 162 (b) 57 (c) 18 (d) 54
  4. 4.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 457 (c) 456 (d) 447
  5. 5.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 429 (b) 420 (c) 430 (d) 358
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 39? (a) 13 (b) 14 (c) 15 (d) 3
  7. 7.How many times is the digit 6 written when you write all the numbers from 1 to 66? (a) 13 (b) 15 (c) 6 (d) 14
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 85? (a) 19 (b) 8 (c) 17 (d) 18
  9. 9.A book has 219 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 438 (b) 549 (c) 540 (d) 550
  10. 10.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) 19 (b) 60 (c) 57 (d) 171
  11. 11.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) 90 (b) 30 (c) 10 (d) 33
  12. 12.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  13. 13.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 288 (b) 324 (c) 325 (d) 315
  14. 14.A book has 102 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 198 (b) 189 (c) 199 (d) 204
  15. 15.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  16. 16.A book has 141 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 316 (b) 282 (c) 315 (d) 306
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 41? (a) 2 (b) 4 (c) 5 (d) 3
  18. 18.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) 9 (c) 81 (d) 27
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 8 (b) 18 (c) 19 (d) 20
  20. 20.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 5 (d) 6
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 19 (b) 21 (c) 20 (d) 9
  22. 22.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) 33 (b) 99 (c) 11 (d) 36
  23. 23.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 20 (b) 19 (c) 9 (d) 18
  24. 24.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) 63 (b) 189 (c) 21 (d) 66
  25. 25.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  26. 26.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) 20 (d) 63
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 72? (a) 7 (b) 18 (c) 17 (d) 16
  28. 28.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) 45 (b) 126 (c) 14 (d) 42
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 18 (b) 16 (c) 6 (d) 17
  30. 30.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) 600 (c) 609 (d) 610
  31. 31.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 10 (c) 1 (d) 2
  32. 32.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) 24 (b) 27 (c) 8 (d) 72
  33. 33.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 2 (c) 1 (d) 18
  34. 34.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 426 (c) 531 (d) 532
  35. 35.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
  36. 36.A book has 249 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 639 (b) 640 (c) 630 (d) 498
  37. 37.A book has 81 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 144 (b) 153 (c) 154 (d) 162
  38. 38.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 14 (b) 8 (c) 11 (d) 13
  39. 39.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) 21 (c) 24 (d) 63
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 19 (d) 20

Answer key

  1. 19
  2. 3
  3. 54
  4. 456
  5. 429
  6. 14
  7. 14
  8. 18
  9. 549
  10. 57
  11. 30
  12. 3
  13. 324
  14. 198
  15. 8
  16. 315
  17. 4
  18. 27
  19. 19
  20. 5
  21. 20
  22. 33
  23. 19
  24. 63
  25. 7
  26. 60
  27. 17
  28. 42
  29. 17
  30. 609
  31. 2
  32. 24
  33. 2
  34. 531
  35. 69
  36. 639
  37. 153
  38. 13
  39. 21
  40. 19

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