← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 56 · 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 6 written when you write all the numbers from 1 to 94? (a) 18 (b) 19 (c) 9 (d) 20
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 96? (a) 19 (b) 20 (c) 18 (d) 9
  3. 3.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 10 (d) 7
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 93? (a) 20 (b) 9 (c) 19 (d) 21
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 3 (d) 10
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 59? (a) 5 (b) 16 (c) 15 (d) 17
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 93? (a) 9 (b) 19 (c) 21 (d) 20
  8. 8.A book has 230 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 583 (b) 582 (c) 460 (d) 573
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 20 (b) 19 (c) 18 (d) 8
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 2 (c) 10 (d) 3
  11. 11.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 40 (c) 39 (d) 30
  12. 12.A book has 161 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 366 (b) 375 (c) 322 (d) 376
  13. 13.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) 171 (c) 57 (d) 60
  14. 14.A book has 168 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 336 (b) 396 (c) 387 (d) 397
  15. 15.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) 81 (c) 9 (d) 27
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 72? (a) 16 (b) 18 (c) 7 (d) 17
  17. 17.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) 180 (c) 60 (d) 20
  18. 18.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) 98 (c) 89 (d) 90
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 33? (a) 9 (b) 3 (c) 7 (d) 8
  20. 20.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 435 (c) 426 (d) 362
  21. 21.The numbers 18 to 26 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 69 (b) 22 (c) 66 (d) 198
  22. 22.How many times is the digit 5 written when you write all the numbers from 1 to 58? (a) 5 (b) 16 (c) 15 (d) 14
  23. 23.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 9 (d) 19
  24. 24.A book has 178 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 427 (b) 356 (c) 417 (d) 426
  25. 25.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) 15 (c) 45 (d) 135
  26. 26.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 9 (d) 8
  27. 27.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) 18 (c) 57 (d) 54
  28. 28.A book has 156 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 312 (b) 361 (c) 351 (d) 360
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 5 (b) 12 (c) 14 (d) 13
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 8 (b) 11 (c) 10 (d) 9
  31. 31.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 254 (b) 273 (c) 274 (d) 264
  32. 32.A book has 231 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 576 (b) 462 (c) 585 (d) 586
  33. 33.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) 13 (c) 117 (d) 42
  34. 34.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) 6 (c) 54 (d) 18
  35. 35.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) 36 (c) 35 (d) 44
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 3 (d) 5
  37. 37.How many times is the digit 5 written when you write all the numbers from 1 to 76? (a) 17 (b) 19 (c) 7 (d) 18
  38. 38.How many times is the digit 2 written when you write all the numbers from 1 to 77? (a) 19 (b) 7 (c) 18 (d) 17
  39. 39.How many times is the digit 2 written when you write all the numbers from 1 to 85? (a) 19 (b) 20 (c) 8 (d) 18
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 6 (b) 8 (c) 7 (d) 9

Answer key

  1. 19
  2. 19
  3. 7
  4. 20
  5. 4
  6. 16
  7. 20
  8. 582
  9. 19
  10. 2
  11. 39
  12. 375
  13. 57
  14. 396
  15. 27
  16. 17
  17. 60
  18. 89
  19. 8
  20. 435
  21. 66
  22. 15
  23. 20
  24. 426
  25. 45
  26. 9
  27. 54
  28. 360
  29. 13
  30. 10
  31. 273
  32. 585
  33. 39
  34. 18
  35. 35
  36. 4
  37. 18
  38. 18
  39. 19
  40. 8

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