← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 502 · 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 9 written when you write all the numbers from 1 to 85? (a) 7 (b) 6 (c) 9 (d) 8
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 72? (a) 17 (b) 7 (c) 18 (d) 16
  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) 60 (c) 63 (d) 180
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 64? (a) 6 (b) 4 (c) 7 (d) 5
  5. 5.How many times is the digit 8 written when you write all the numbers from 1 to 72? (a) 8 (b) 5 (c) 6 (d) 7
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 74? (a) 17 (b) 19 (c) 7 (d) 18
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 84? (a) 17 (b) 18 (c) 8 (d) 19
  8. 8.How many times is the digit 2 written when you write all the numbers from 1 to 51? (a) 5 (b) 16 (c) 15 (d) 14
  9. 9.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) 198 (b) 66 (c) 69 (d) 22
  10. 10.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 350 (b) 417 (c) 418 (d) 408
  11. 11.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) 7 (b) 63 (c) 24 (d) 21
  12. 12.How many times is the digit 1 written when you write all the numbers from 1 to 88? (a) 20 (b) 8 (c) 18 (d) 19
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 8 (b) 7 (c) 6 (d) 5
  14. 14.How many times is the digit 6 written when you write all the numbers from 1 to 70? (a) 16 (b) 17 (c) 7 (d) 18
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 99? (a) 19 (b) 9 (c) 21 (d) 20
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 53? (a) 5 (b) 9 (c) 10 (d) 7
  17. 17.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 4 (c) 3 (d) 2
  18. 18.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) 36 (c) 39 (d) 108
  19. 19.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 10 (c) 6 (d) 5
  20. 20.A book has 58 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 98 (b) 107 (c) 116 (d) 108
  21. 21.A book has 114 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 234 (b) 225 (c) 235 (d) 228
  22. 22.How many times is the digit 3 written when you write all the numbers from 1 to 85? (a) 18 (b) 19 (c) 20 (d) 8
  23. 23.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) 36 (c) 99 (d) 33
  24. 24.A book has 40 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 72 (c) 62 (d) 71
  25. 25.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  26. 26.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 2 (c) 3 (d) 1
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 61? (a) 6 (b) 15 (c) 16 (d) 17
  28. 28.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 8 (d) 10
  29. 29.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 580 (c) 570 (d) 579
  30. 30.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  31. 31.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 10 (d) 4
  32. 32.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  33. 33.A book has 179 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 420 (b) 430 (c) 358 (d) 429
  34. 34.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) 57 (b) 18 (c) 162 (d) 54
  35. 35.A book has 189 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 450 (b) 378 (c) 460 (d) 459
  36. 36.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 19 (b) 18 (c) 7 (d) 17
  37. 37.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 110 (b) 100 (c) 109 (d) 118
  38. 38.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 268 (c) 294 (d) 295
  39. 39.A book has 97 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 186 (b) 176 (c) 185 (d) 194
  40. 40.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 3 (c) 10 (d) 1

Answer key

  1. 8
  2. 17
  3. 60
  4. 6
  5. 7
  6. 18
  7. 18
  8. 15
  9. 66
  10. 417
  11. 21
  12. 19
  13. 7
  14. 17
  15. 20
  16. 9
  17. 3
  18. 36
  19. 6
  20. 107
  21. 234
  22. 19
  23. 33
  24. 71
  25. 4
  26. 2
  27. 16
  28. 9
  29. 579
  30. 7
  31. 4
  32. 6
  33. 429
  34. 54
  35. 459
  36. 18
  37. 109
  38. 294
  39. 185
  40. 2

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