← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 132 · 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 2? (a) 3 (b) 1 (c) 10 (d) 2
  2. 2.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 3 (b) 4 (c) 5 (d) 6
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 31? (a) 4 (b) 1 (c) 2 (d) 3
  4. 4.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  6. 6.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 77? (a) 16 (b) 17 (c) 7 (d) 15
  8. 8.A book has 132 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 289 (c) 264 (d) 288
  9. 9.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) 18 (c) 54 (d) 6
  10. 10.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) 171 (b) 19 (c) 60 (d) 57
  11. 11.How many times is the digit 6 written when you write all the numbers from 1 to 46? (a) 4 (b) 6 (c) 5 (d) 3
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  13. 13.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) 63 (b) 189 (c) 21 (d) 66
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 44? (a) 2 (b) 3 (c) 5 (d) 4
  15. 15.How many times is the digit 5 written when you write all the numbers from 1 to 68? (a) 6 (b) 18 (c) 17 (d) 16
  16. 16.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) 22 (b) 69 (c) 66 (d) 198
  17. 17.How many times is the digit 1 written when you write all the numbers from 1 to 84? (a) 19 (b) 18 (c) 20 (d) 8
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 5 (b) 3 (c) 4 (d) 2
  19. 19.A book has 142 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 319 (b) 309 (c) 284 (d) 318
  20. 20.How many times is the digit 7 written when you write all the numbers from 1 to 55? (a) 4 (b) 5 (c) 3 (d) 6
  21. 21.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) 24 (b) 72 (c) 8 (d) 27
  22. 22.A book has 94 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 188 (b) 180 (c) 179 (d) 170
  23. 23.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) 16 (b) 51 (c) 144 (d) 48
  24. 24.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 4 (c) 3 (d) 16
  25. 25.A book has 48 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 88 (c) 96 (d) 87
  26. 26.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 346 (b) 402 (c) 411 (d) 412
  27. 27.A book has 174 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 414 (c) 415 (d) 405
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 41? (a) 5 (b) 2 (c) 4 (d) 3
  29. 29.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 2 (d) 3
  30. 30.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 18 (c) 1 (d) 3
  31. 31.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 15 (b) 9 (c) 16 (d) 13
  32. 32.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 6 (d) 4
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 17 (d) 16
  34. 34.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 42 (b) 24 (c) 34 (d) 33
  35. 35.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 69 (c) 60 (d) 78
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 40? (a) 3 (b) 4 (c) 5 (d) 2
  37. 37.A book has 98 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 187 (c) 188 (d) 196
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 87? (a) 20 (b) 18 (c) 8 (d) 19
  39. 39.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 40? (a) 13 (b) 4 (c) 14 (d) 15

Answer key

  1. 2
  2. 5
  3. 3
  4. 4
  5. 8
  6. 5
  7. 16
  8. 288
  9. 18
  10. 57
  11. 5
  12. 9
  13. 63
  14. 4
  15. 17
  16. 66
  17. 19
  18. 4
  19. 318
  20. 5
  21. 24
  22. 179
  23. 48
  24. 4
  25. 87
  26. 411
  27. 414
  28. 4
  29. 3
  30. 2
  31. 15
  32. 5
  33. 17
  34. 33
  35. 69
  36. 4
  37. 187
  38. 19
  39. 7
  40. 14

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