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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 60 · 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 7 written when you write all the numbers from 1 to 32? (a) 2 (b) 3 (c) 1 (d) 4
  2. 2.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 13 (b) 4 (c) 12 (d) 14
  3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 79? (a) 18 (b) 17 (c) 19 (d) 7
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 5 (d) 14
  5. 5.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 7 (d) 8
  6. 6.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) 108 (b) 12 (c) 36 (d) 39
  7. 7.The numbers 10 to 18 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 14 (b) 126 (c) 42 (d) 45
  8. 8.How many times is the digit 4 written when you write all the numbers from 1 to 96? (a) 19 (b) 21 (c) 20 (d) 9
  9. 9.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
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 6 (b) 7 (c) 10 (d) 8
  11. 11.A book has 22 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 26 (b) 36 (c) 44 (d) 35
  12. 12.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 7 (b) 19 (c) 17 (d) 18
  13. 13.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 12 (c) 7 (d) 8
  14. 14.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 15 (c) 5 (d) 6
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 80? (a) 19 (b) 8 (c) 18 (d) 17
  16. 16.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) 8 (b) 24 (c) 72 (d) 27
  17. 17.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  18. 18.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 13 (c) 8 (d) 6
  19. 19.How many times is the digit 6 written when you write all the numbers from 1 to 31? (a) 3 (b) 4 (c) 2 (d) 1
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 80? (a) 8 (b) 19 (c) 18 (d) 17
  21. 21.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 4 (c) 16 (d) 5
  22. 22.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) 60 (c) 57 (d) 19
  23. 23.How many two-digit numbers have digits that add up to 16? (a) 3 (b) 4 (c) 2 (d) 17
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 73? (a) 18 (b) 17 (c) 7 (d) 16
  25. 25.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 10 (c) 5 (d) 4
  26. 26.How many times is the digit 2 written when you write all the numbers from 1 to 71? (a) 17 (b) 18 (c) 16 (d) 7
  27. 27.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) 18 (b) 21 (c) 54 (d) 6
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 18 (b) 7 (c) 19 (d) 17
  29. 29.A book has 100 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 183 (b) 193 (c) 200 (d) 192
  30. 30.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
  31. 31.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 4 (c) 10 (d) 3
  32. 32.How many times is the digit 7 written when you write all the numbers from 1 to 56? (a) 5 (b) 6 (c) 4 (d) 3
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  34. 34.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  35. 35.How many times is the digit 9 written when you write all the numbers from 1 to 88? (a) 9 (b) 8 (c) 6 (d) 7
  36. 36.How many times is the digit 2 written when you write all the numbers from 1 to 32? (a) 14 (b) 13 (c) 3 (d) 15
  37. 37.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) 75 (b) 24 (c) 216 (d) 72
  38. 38.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) 10 (b) 33 (c) 30 (d) 90
  39. 39.How many times is the digit 4 written when you write all the numbers from 1 to 97? (a) 21 (b) 9 (c) 20 (d) 19
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 53? (a) 6 (b) 4 (c) 5 (d) 3

Answer key

  1. 3
  2. 13
  3. 18
  4. 15
  5. 8
  6. 36
  7. 42
  8. 20
  9. 54
  10. 7
  11. 35
  12. 18
  13. 8
  14. 5
  15. 18
  16. 24
  17. 6
  18. 7
  19. 3
  20. 18
  21. 4
  22. 57
  23. 3
  24. 17
  25. 5
  26. 17
  27. 18
  28. 18
  29. 192
  30. 21
  31. 4
  32. 5
  33. 9
  34. 9
  35. 8
  36. 14
  37. 72
  38. 30
  39. 20
  40. 5

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