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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 710 · 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) 13 (b) 8 (c) 7 (d) 6
  2. 2.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 19 (b) 18 (c) 17 (d) 7
  3. 3.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) 54 (b) 51 (c) 153 (d) 17
  4. 4.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 5 (d) 10
  5. 5.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) 69 (b) 22 (c) 66 (d) 198
  6. 6.How many times is the digit 3 written when you write all the numbers from 1 to 78? (a) 17 (b) 18 (c) 19 (d) 7
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 51? (a) 6 (b) 5 (c) 8 (d) 7
  8. 8.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) 33 (b) 36 (c) 99 (d) 11
  9. 9.How many times is the digit 1 written when you write all the numbers from 1 to 71? (a) 19 (b) 7 (c) 17 (d) 18
  10. 10.How many times is the digit 1 written when you write all the numbers from 1 to 46? (a) 16 (b) 14 (c) 4 (d) 15
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 77? (a) 8 (b) 5 (c) 6 (d) 7
  12. 12.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 17 (b) 16 (c) 15 (d) 6
  13. 13.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 14 (c) 5 (d) 6
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  15. 15.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) 60 (b) 20 (c) 63 (d) 180
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 92? (a) 19 (b) 9 (c) 20 (d) 21
  17. 17.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) 51 (b) 48 (c) 144 (d) 16
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 18 (b) 20 (c) 19 (d) 8
  19. 19.How many times is the digit 1 written when you write all the numbers from 1 to 38? (a) 15 (b) 3 (c) 13 (d) 14
  20. 20.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 6 (c) 7 (d) 10
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 54? (a) 17 (b) 15 (c) 5 (d) 16
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 2 (c) 4 (d) 3
  23. 23.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 18 (d) 3
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 21 (b) 20 (c) 9 (d) 19
  25. 25.The numbers 5 to 13 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 27 (b) 9 (c) 30 (d) 81
  26. 26.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 410 (b) 508 (c) 498 (d) 507
  27. 27.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  28. 28.How many times is the digit 6 written when you write all the numbers from 1 to 68? (a) 15 (b) 6 (c) 16 (d) 17
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 7 (c) 9 (d) 8
  30. 30.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) 45 (b) 42 (c) 126 (d) 14
  31. 31.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) 6 (c) 54 (d) 21
  32. 32.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 9 (d) 21
  33. 33.How many two-digit numbers have digits that add up to 16? (a) 17 (b) 2 (c) 3 (d) 4
  34. 34.A book has 111 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 216 (b) 225 (c) 222 (d) 226
  35. 35.A book has 244 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 625 (b) 488 (c) 624 (d) 615
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 85? (a) 18 (b) 20 (c) 8 (d) 19
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 83? (a) 18 (b) 19 (c) 8 (d) 20
  38. 38.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 16 (c) 4 (d) 3
  39. 39.How many times is the digit 1 written when you write all the numbers from 1 to 45? (a) 4 (b) 14 (c) 16 (d) 15
  40. 40.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 9 (c) 10 (d) 8

Answer key

  1. 7
  2. 18
  3. 51
  4. 6
  5. 66
  6. 18
  7. 7
  8. 33
  9. 18
  10. 15
  11. 7
  12. 16
  13. 6
  14. 5
  15. 60
  16. 20
  17. 48
  18. 19
  19. 14
  20. 7
  21. 16
  22. 3
  23. 2
  24. 20
  25. 27
  26. 507
  27. 4
  28. 16
  29. 8
  30. 42
  31. 18
  32. 20
  33. 3
  34. 225
  35. 624
  36. 19
  37. 19
  38. 4
  39. 15
  40. 9

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