← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 661 · 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.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 348 (c) 339 (d) 349
  2. 2.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 192 (b) 201 (c) 206 (d) 202
  3. 3.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) 50 (d) 41
  4. 4.A book has 52 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 95 (c) 96 (d) 104
  5. 5.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 180 (b) 170 (c) 179 (d) 188
  6. 6.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  7. 7.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 13 (b) 15 (c) 4 (d) 14
  8. 8.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) 57 (b) 19 (c) 171 (d) 60
  9. 9.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 4 (b) 5 (c) 6 (d) 3
  10. 10.A book has 53 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 106 (b) 88 (c) 98 (d) 97
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 34? (a) 4 (b) 2 (c) 5 (d) 3
  12. 12.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 20 (d) 19
  14. 14.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 5 (c) 4 (d) 16
  15. 15.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 37? (a) 2 (b) 5 (c) 4 (d) 3
  17. 17.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 10 (c) 2 (d) 3
  18. 18.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 298 (b) 330 (c) 339 (d) 340
  19. 19.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 207 (c) 217 (d) 324
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 61? (a) 5 (b) 7 (c) 4 (d) 6
  21. 21.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 366 (c) 367 (d) 316
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 95? (a) 20 (b) 21 (c) 19 (d) 9
  23. 23.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 5 (b) 7 (c) 6 (d) 4
  24. 24.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 6 (d) 7
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 17 (d) 18
  26. 26.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 52? (a) 5 (b) 17 (c) 16 (d) 15
  28. 28.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 12 (b) 13 (c) 14 (d) 3
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 8 (d) 9
  30. 30.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 222 (c) 226 (d) 225
  31. 31.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) 69 (d) 207
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 5 (d) 10
  33. 33.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) 99 (b) 33 (c) 36 (d) 11
  34. 34.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) 394 (c) 474 (d) 483
  35. 35.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) 15 (b) 48 (c) 135 (d) 45
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 83? (a) 8 (b) 19 (c) 17 (d) 18
  37. 37.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 382 (b) 326 (c) 372 (d) 381
  38. 38.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) 24 (b) 75 (c) 72 (d) 216
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 8 (b) 6 (c) 7 (d) 5
  40. 40.A book has 71 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 142 (c) 133 (d) 124

Answer key

  1. 348
  2. 201
  3. 41
  4. 95
  5. 179
  6. 2
  7. 14
  8. 57
  9. 5
  10. 97
  11. 4
  12. 3
  13. 20
  14. 4
  15. 7
  16. 4
  17. 2
  18. 339
  19. 216
  20. 6
  21. 366
  22. 20
  23. 6
  24. 6
  25. 18
  26. 4
  27. 16
  28. 13
  29. 8
  30. 225
  31. 69
  32. 5
  33. 33
  34. 483
  35. 45
  36. 18
  37. 381
  38. 72
  39. 7
  40. 133

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