← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 3 · 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 3? (a) 3 (b) 10 (c) 4 (d) 2
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 2 (c) 1 (d) 10
  3. 3.How many times is the digit 3 written when you write all the numbers from 1 to 75? (a) 7 (b) 18 (c) 19 (d) 17
  4. 4.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  5. 5.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 378 (b) 450 (c) 459 (d) 460
  6. 6.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) 207 (b) 69 (c) 23 (d) 72
  7. 7.A book has 106 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 211 (b) 201 (c) 210 (d) 212
  8. 8.How many times is the digit 7 written when you write all the numbers from 1 to 45? (a) 2 (b) 3 (c) 4 (d) 5
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 79? (a) 19 (b) 17 (c) 7 (d) 18
  11. 11.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 8 (c) 7 (d) 12
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 71? (a) 7 (b) 16 (c) 17 (d) 18
  13. 13.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) 60 (b) 20 (c) 63 (d) 180
  14. 14.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) 39 (c) 36 (d) 108
  15. 15.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 16 (d) 3
  16. 16.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  17. 17.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 14 (b) 4 (c) 13 (d) 15
  18. 18.How many two-digit numbers have digits that add up to 10? (a) 8 (b) 10 (c) 11 (d) 9
  19. 19.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 595 (c) 585 (d) 468
  20. 20.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) 144 (b) 51 (c) 48 (d) 16
  21. 21.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 447 (b) 376 (c) 456 (d) 457
  22. 22.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
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 33? (a) 4 (b) 2 (c) 1 (d) 3
  24. 24.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 10 (d) 11
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 53? (a) 15 (b) 5 (c) 17 (d) 16
  26. 26.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 157 (c) 158 (d) 166
  27. 27.A book has 133 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 291 (b) 292 (c) 282 (d) 266
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 31? (a) 2 (b) 4 (c) 3 (d) 1
  29. 29.How many times is the digit 3 written when you write all the numbers from 1 to 44? (a) 4 (b) 16 (c) 15 (d) 14
  30. 30.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) 21 (b) 24 (c) 63 (d) 7
  31. 31.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) 13 (b) 117 (c) 39 (d) 42
  32. 32.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 138 (c) 156 (d) 147
  33. 33.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) 45 (d) 48
  34. 34.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 415 (b) 405 (c) 348 (d) 414
  35. 35.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 6 (d) 4
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 89? (a) 18 (b) 8 (c) 19 (d) 20
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 4 (b) 9 (c) 11 (d) 10
  38. 38.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 56 (c) 74 (d) 66
  39. 39.A book has 165 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 387 (b) 378 (c) 388 (d) 330
  40. 40.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 62 (b) 71 (c) 72 (d) 80

Answer key

  1. 3
  2. 2
  3. 18
  4. 7
  5. 459
  6. 69
  7. 210
  8. 4
  9. 4
  10. 18
  11. 8
  12. 17
  13. 60
  14. 36
  15. 4
  16. 2
  17. 14
  18. 9
  19. 594
  20. 48
  21. 456
  22. 18
  23. 3
  24. 9
  25. 16
  26. 157
  27. 291
  28. 3
  29. 15
  30. 21
  31. 39
  32. 147
  33. 45
  34. 414
  35. 5
  36. 19
  37. 10
  38. 65
  39. 387
  40. 71

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