← Number puzzles and digit counting lesson New set →

Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 440 · 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 3 written when you write all the numbers from 1 to 33? (a) 3 (b) 9 (c) 8 (d) 7
  2. 2.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) 18 (b) 54 (c) 162 (d) 57
  3. 3.How many times is the digit 6 written when you write all the numbers from 1 to 59? (a) 7 (b) 4 (c) 6 (d) 5
  4. 4.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 4 (b) 6 (c) 5 (d) 3
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 79? (a) 18 (b) 19 (c) 17 (d) 7
  6. 6.How many times is the digit 2 written when you write all the numbers from 1 to 87? (a) 8 (b) 20 (c) 19 (d) 18
  7. 7.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  8. 8.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) 439 (c) 429 (d) 438
  9. 9.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 118 (b) 126 (c) 108 (d) 117
  10. 10.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) 72 (b) 24 (c) 8 (d) 27
  11. 11.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 190 (c) 181 (d) 182
  12. 12.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) 39 (b) 12 (c) 108 (d) 36
  13. 13.How many two-digit numbers have digits that add up to 8? (a) 9 (b) 8 (c) 10 (d) 7
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 5 (b) 17 (c) 16 (d) 15
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 7 (b) 19 (c) 17 (d) 18
  16. 16.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 6 (d) 5
  17. 17.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) 189 (b) 63 (c) 66 (d) 21
  18. 18.How many times is the digit 5 written when you write all the numbers from 1 to 38? (a) 2 (b) 5 (c) 3 (d) 4
  19. 19.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 15 (c) 18 (d) 45
  20. 20.How many times is the digit 8 written when you write all the numbers from 1 to 48? (a) 5 (b) 3 (c) 6 (d) 4
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 10 (c) 9 (d) 8
  22. 22.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 5 (d) 3
  23. 23.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 34 (c) 52 (d) 43
  24. 24.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 36 (c) 26 (d) 35
  25. 25.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) 171 (c) 19 (d) 57
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 18 (b) 17 (c) 7 (d) 19
  27. 27.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 12 (b) 14 (c) 15 (d) 9
  28. 28.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  29. 29.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 628 (b) 627 (c) 618 (d) 490
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 31? (a) 13 (b) 14 (c) 3 (d) 12
  31. 31.A book has 227 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 573 (b) 564 (c) 574 (d) 454
  32. 32.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 94 (b) 93 (c) 84 (d) 102
  33. 33.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) 21 (d) 24
  34. 34.How many times is the digit 8 written when you write all the numbers from 1 to 89? (a) 20 (b) 19 (c) 8 (d) 18
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 17 (b) 19 (c) 7 (d) 18
  36. 36.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 12 (b) 13 (c) 14 (d) 4
  37. 37.A book has 115 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 230 (b) 228 (c) 238 (d) 237
  38. 38.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) 63 (b) 60 (c) 20 (d) 180
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 67? (a) 4 (b) 5 (c) 6 (d) 7
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 36? (a) 14 (b) 3 (c) 15 (d) 13

Answer key

  1. 8
  2. 54
  3. 6
  4. 5
  5. 18
  6. 19
  7. 7
  8. 438
  9. 117
  10. 24
  11. 181
  12. 36
  13. 8
  14. 16
  15. 18
  16. 6
  17. 63
  18. 4
  19. 15
  20. 5
  21. 9
  22. 4
  23. 43
  24. 35
  25. 57
  26. 18
  27. 14
  28. 2
  29. 627
  30. 13
  31. 573
  32. 93
  33. 21
  34. 19
  35. 18
  36. 13
  37. 237
  38. 60
  39. 6
  40. 14

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