← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 550 · 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 235 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 598 (b) 588 (c) 597 (d) 470
  2. 2.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 5 (b) 16 (c) 14 (d) 15
  3. 3.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 5 (d) 3
  4. 4.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 86 (c) 77 (d) 68
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 4 (d) 5
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 64? (a) 5 (b) 6 (c) 7 (d) 4
  7. 7.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 8 (d) 10
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 67? (a) 16 (b) 6 (c) 18 (d) 17
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 53? (a) 4 (b) 6 (c) 3 (d) 5
  10. 10.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 618 (c) 619 (d) 609
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 10 (d) 3
  12. 12.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 150 (c) 159 (d) 160
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 72? (a) 5 (b) 7 (c) 6 (d) 8
  14. 14.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 2 (d) 1
  15. 15.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  16. 16.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 67 (c) 76 (d) 58
  17. 17.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 56 (b) 64 (c) 46 (d) 55
  18. 18.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 531 (c) 532 (d) 522
  19. 19.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 1 (d) 3
  20. 20.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) 11 (b) 33 (c) 36 (d) 99
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 62? (a) 17 (b) 6 (c) 16 (d) 18
  22. 22.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) 90 (b) 10 (c) 33 (d) 30
  23. 23.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) 216 (c) 72 (d) 75
  24. 24.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) 51 (b) 144 (c) 48 (d) 16
  25. 25.How many times is the digit 7 written when you write all the numbers from 1 to 72? (a) 8 (b) 11 (c) 7 (d) 10
  26. 26.A book has 92 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 175 (c) 184 (d) 176
  27. 27.How many two-digit numbers have digits that add up to 13? (a) 5 (b) 7 (c) 14 (d) 6
  28. 28.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) 63 (c) 21 (d) 189
  29. 29.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 4 (b) 3 (c) 6 (d) 5
  30. 30.A book has 124 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 255 (b) 248 (c) 264 (d) 265
  31. 31.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 82 (b) 100 (c) 92 (d) 91
  32. 32.A book has 123 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 246 (b) 252 (c) 261 (d) 262
  33. 33.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 237 (b) 238 (c) 228 (d) 230
  34. 34.A book has 240 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 613 (b) 603 (c) 612 (d) 480
  35. 35.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 96 (b) 105 (c) 114 (d) 106
  36. 36.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) 60 (b) 19 (c) 171 (d) 57
  37. 37.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 59? (a) 17 (b) 5 (c) 16 (d) 15
  39. 39.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  40. 40.How many times is the digit 9 written when you write all the numbers from 1 to 87? (a) 8 (b) 9 (c) 6 (d) 7

Answer key

  1. 597
  2. 15
  3. 4
  4. 77
  5. 4
  6. 6
  7. 7
  8. 17
  9. 5
  10. 618
  11. 3
  12. 159
  13. 7
  14. 2
  15. 9
  16. 67
  17. 55
  18. 531
  19. 2
  20. 33
  21. 17
  22. 30
  23. 72
  24. 48
  25. 10
  26. 175
  27. 6
  28. 63
  29. 5
  30. 264
  31. 91
  32. 261
  33. 237
  34. 612
  35. 105
  36. 57
  37. 3
  38. 16
  39. 8
  40. 8

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