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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 324 · 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 12? (a) 6 (b) 8 (c) 13 (d) 7
  2. 2.The numbers 13 to 21 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) 17 (c) 54 (d) 153
  3. 3.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  4. 4.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 8 (c) 9 (d) 10
  5. 5.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 13 (b) 42 (c) 117 (d) 39
  6. 6.A book has 200 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 483 (b) 492 (c) 493 (d) 400
  7. 7.How many two-digit numbers have digits that add up to 11? (a) 9 (b) 7 (c) 8 (d) 12
  8. 8.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 3 (c) 4 (d) 5
  9. 9.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 1 (c) 3 (d) 2
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 73? (a) 5 (b) 7 (c) 8 (d) 6
  11. 11.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 5 (c) 4 (d) 10
  12. 12.A book has 37 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 65 (b) 56 (c) 66 (d) 74
  13. 13.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) 57 (b) 19 (c) 171 (d) 60
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 58? (a) 16 (b) 15 (c) 17 (d) 5
  15. 15.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 7 (b) 5 (c) 4 (d) 6
  16. 16.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 4 (b) 3 (c) 6 (d) 5
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 94? (a) 18 (b) 20 (c) 9 (d) 19
  18. 18.How many times is the digit 3 written when you write all the numbers from 1 to 67? (a) 17 (b) 18 (c) 6 (d) 16
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 31? (a) 3 (b) 6 (c) 5 (d) 4
  20. 20.How many times is the digit 4 written when you write all the numbers from 1 to 39? (a) 5 (b) 2 (c) 4 (d) 3
  21. 21.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) 108 (c) 36 (d) 12
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 87? (a) 8 (b) 18 (c) 20 (d) 19
  23. 23.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 3 (c) 2 (d) 4
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 19 (b) 20 (c) 8 (d) 18
  25. 25.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) 33 (b) 10 (c) 30 (d) 90
  26. 26.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) 66 (c) 189 (d) 21
  27. 27.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 39 (c) 30 (d) 40
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 70? (a) 7 (b) 17 (c) 16 (d) 18
  29. 29.How many times is the digit 2 written when you write all the numbers from 1 to 86? (a) 19 (b) 18 (c) 8 (d) 20
  30. 30.How many times is the digit 5 written when you write all the numbers from 1 to 77? (a) 18 (b) 19 (c) 7 (d) 17
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 93? (a) 18 (b) 19 (c) 9 (d) 20
  32. 32.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) 63 (b) 24 (c) 21 (d) 7
  33. 33.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
  34. 34.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 68 (b) 59 (c) 60 (d) 50
  35. 35.A book has 78 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 148 (b) 138 (c) 147 (d) 156
  36. 36.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 9 (d) 8
  37. 37.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) 20 (c) 180 (d) 60
  38. 38.How many times is the digit 6 written when you write all the numbers from 1 to 45? (a) 2 (b) 3 (c) 4 (d) 5
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 4 (b) 6 (c) 3 (d) 5
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 42? (a) 14 (b) 4 (c) 15 (d) 13

Answer key

  1. 7
  2. 51
  3. 6
  4. 8
  5. 39
  6. 492
  7. 8
  8. 4
  9. 2
  10. 7
  11. 4
  12. 65
  13. 57
  14. 16
  15. 6
  16. 5
  17. 19
  18. 17
  19. 5
  20. 4
  21. 36
  22. 19
  23. 3
  24. 19
  25. 30
  26. 63
  27. 39
  28. 17
  29. 19
  30. 18
  31. 19
  32. 21
  33. 459
  34. 59
  35. 147
  36. 9
  37. 60
  38. 4
  39. 5
  40. 14

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