← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 442 · 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 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) 60 (c) 180 (d) 20
  2. 2.A book has 192 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 459 (b) 469 (c) 468 (d) 384
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 4 (c) 6 (d) 15
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 6 (c) 8 (d) 13
  5. 5.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  6. 6.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 90 (b) 72 (c) 82 (d) 81
  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) 48 (b) 45 (c) 135 (d) 15
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 51? (a) 3 (b) 6 (c) 5 (d) 4
  9. 9.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) 39 (b) 42 (c) 117 (d) 13
  10. 10.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) 90 (d) 30
  11. 11.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 44 (c) 35 (d) 36
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 17 (b) 8 (c) 18 (d) 19
  13. 13.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) 162 (c) 154 (d) 153
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 3 (b) 14 (c) 13 (d) 15
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  16. 16.A book has 241 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 615 (b) 482 (c) 616 (d) 606
  17. 17.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) 27 (d) 81
  18. 18.How many times is the digit 2 written when you write all the numbers from 1 to 48? (a) 4 (b) 16 (c) 14 (d) 15
  19. 19.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 48 (c) 57 (d) 58
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 16 (b) 5 (c) 17 (d) 15
  21. 21.A book has 144 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 324 (b) 315 (c) 325 (d) 288
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 4 (b) 2 (c) 3 (d) 1
  23. 23.A book has 41 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 82 (c) 74 (d) 73
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 52? (a) 5 (b) 9 (c) 6 (d) 8
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 20 (b) 19 (c) 18 (d) 8
  26. 26.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 375 (c) 366 (d) 322
  27. 27.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) 189 (c) 21 (d) 63
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 4 (b) 2 (c) 3 (d) 5
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 76? (a) 19 (b) 17 (c) 18 (d) 7
  30. 30.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 390 (b) 477 (c) 468 (d) 478
  31. 31.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 186 (c) 177 (d) 168
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 87? (a) 19 (b) 8 (c) 20 (d) 18
  33. 33.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 562 (b) 561 (c) 446 (d) 552
  34. 34.A book has 167 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 394 (b) 393 (c) 384 (d) 334
  35. 35.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) 18 (c) 45 (d) 15
  36. 36.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 6 (d) 8
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 18 (b) 8 (c) 19 (d) 20
  38. 38.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) 42 (c) 14 (d) 126
  39. 39.A book has 204 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 505 (b) 495 (c) 504 (d) 408
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 6 (b) 17 (c) 18 (d) 16

Answer key

  1. 60
  2. 468
  3. 5
  4. 7
  5. 2
  6. 81
  7. 45
  8. 5
  9. 39
  10. 30
  11. 35
  12. 18
  13. 153
  14. 14
  15. 9
  16. 615
  17. 27
  18. 15
  19. 57
  20. 16
  21. 324
  22. 3
  23. 73
  24. 8
  25. 19
  26. 375
  27. 63
  28. 4
  29. 18
  30. 477
  31. 177
  32. 19
  33. 561
  34. 393
  35. 15
  36. 7
  37. 19
  38. 42
  39. 504
  40. 17

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