← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 918 · 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 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) 75 (b) 24 (c) 72 (d) 216
  2. 2.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 8 (d) 10
  3. 3.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) 20 (b) 180 (c) 60 (d) 63
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 20 (b) 19 (c) 21 (d) 9
  5. 5.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) 45 (b) 48 (c) 135 (d) 15
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 15 (b) 14 (c) 16 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 6 (c) 7 (d) 14
  8. 8.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 294 (b) 304 (c) 274 (d) 303
  9. 9.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 147 (b) 138 (c) 148 (d) 156
  10. 10.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 17 (b) 6 (c) 16 (d) 18
  11. 11.A book has 110 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 222 (b) 220 (c) 223 (d) 213
  12. 12.A book has 130 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 283 (b) 273 (c) 260 (d) 282
  13. 13.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 2 (d) 10
  14. 14.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 51 (c) 60 (d) 52
  15. 15.A book has 182 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 364 (b) 429 (c) 438 (d) 439
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 14 (b) 5 (c) 16 (d) 15
  17. 17.A book has 119 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 250 (b) 238 (c) 249 (d) 240
  18. 18.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 3 (d) 1
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 41? (a) 13 (b) 4 (c) 15 (d) 14
  20. 20.How many times is the digit 3 written when you write all the numbers from 1 to 36? (a) 12 (b) 11 (c) 3 (d) 10
  21. 21.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 483 (c) 394 (d) 474
  22. 22.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) 24 (b) 7 (c) 21 (d) 63
  23. 23.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 32 (c) 41 (d) 50
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 4 (c) 5 (d) 3
  25. 25.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 321 (b) 331 (c) 330 (d) 292
  26. 26.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) 8 (b) 24 (c) 27 (d) 72
  27. 27.How many times is the digit 8 written when you write all the numbers from 1 to 82? (a) 9 (b) 12 (c) 8 (d) 11
  28. 28.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
  29. 29.How many times is the digit 4 written when you write all the numbers from 1 to 42? (a) 5 (b) 8 (c) 7 (d) 4
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 61? (a) 15 (b) 6 (c) 17 (d) 16
  31. 31.How many times is the digit 3 written when you write all the numbers from 1 to 54? (a) 16 (b) 15 (c) 5 (d) 17
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 81? (a) 8 (b) 19 (c) 18 (d) 17
  33. 33.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 112 (b) 111 (c) 120 (d) 102
  34. 34.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 5 (c) 6 (d) 10
  35. 35.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 409 (b) 399 (c) 408 (d) 344
  36. 36.A book has 49 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 89 (b) 80 (c) 90 (d) 98
  37. 37.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) 9 (b) 30 (c) 81 (d) 27
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 3 (b) 13 (c) 14 (d) 12
  39. 39.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) 36 (b) 39 (c) 108 (d) 12
  40. 40.A book has 193 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 386 (b) 462 (c) 472 (d) 471

Answer key

  1. 72
  2. 9
  3. 60
  4. 20
  5. 45
  6. 15
  7. 6
  8. 303
  9. 147
  10. 17
  11. 222
  12. 282
  13. 3
  14. 51
  15. 438
  16. 15
  17. 249
  18. 2
  19. 14
  20. 11
  21. 483
  22. 21
  23. 41
  24. 4
  25. 330
  26. 24
  27. 11
  28. 30
  29. 7
  30. 16
  31. 16
  32. 18
  33. 111
  34. 5
  35. 408
  36. 89
  37. 27
  38. 13
  39. 36
  40. 471

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