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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 256 · 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 7? (a) 7 (b) 6 (c) 8 (d) 10
  2. 2.How many times is the digit 8 written when you write all the numbers from 1 to 34? (a) 4 (b) 3 (c) 2 (d) 1
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 44? (a) 9 (b) 4 (c) 10 (d) 11
  4. 4.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) 20 (b) 63 (c) 180 (d) 60
  5. 5.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) 54 (b) 18 (c) 6 (d) 21
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 47? (a) 4 (b) 2 (c) 5 (d) 3
  7. 7.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  8. 8.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) 9 (b) 81 (c) 30 (d) 27
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 7 (b) 5 (c) 6 (d) 8
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 67? (a) 5 (b) 6 (c) 4 (d) 7
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 85? (a) 18 (b) 8 (c) 20 (d) 19
  12. 12.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) 198 (b) 69 (c) 22 (d) 66
  13. 13.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 3 (c) 1 (d) 2
  14. 14.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 10 (c) 3 (d) 4
  15. 15.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 15 (c) 6 (d) 4
  16. 16.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) 39 (b) 42 (c) 117 (d) 13
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 42? (a) 4 (b) 5 (c) 3 (d) 2
  18. 18.A book has 234 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 594 (b) 595 (c) 468 (d) 585
  19. 19.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 4 (d) 5
  20. 20.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 102 (c) 120 (d) 112
  21. 21.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  22. 22.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 18 (b) 19 (c) 20 (d) 9
  23. 23.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  24. 24.How many times is the digit 5 written when you write all the numbers from 1 to 46? (a) 4 (b) 5 (c) 3 (d) 6
  25. 25.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) 45 (c) 126 (d) 42
  26. 26.The numbers 19 to 27 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) 69 (c) 23 (d) 207
  27. 27.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) 36 (b) 99 (c) 33 (d) 11
  28. 28.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 2 (b) 4 (c) 1 (d) 3
  29. 29.A book has 47 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 86 (c) 94 (d) 85
  30. 30.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  31. 31.How many times is the digit 8 written when you write all the numbers from 1 to 55? (a) 3 (b) 5 (c) 6 (d) 4
  32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 50? (a) 3 (b) 6 (c) 5 (d) 4
  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) 24 (c) 21 (d) 63
  34. 34.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 6 (b) 9 (c) 7 (d) 8
  35. 35.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 409 (b) 399 (c) 408 (d) 344
  36. 36.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) 36 (c) 12 (d) 39
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 11 (b) 8 (c) 9 (d) 10
  38. 38.A book has 43 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 86 (b) 78 (c) 77 (d) 68
  39. 39.A book has 135 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 297 (b) 270 (c) 298 (d) 288
  40. 40.How many times is the digit 3 written when you write all the numbers from 1 to 38? (a) 14 (b) 13 (c) 12 (d) 3

Answer key

  1. 7
  2. 3
  3. 10
  4. 60
  5. 18
  6. 4
  7. 6
  8. 27
  9. 7
  10. 6
  11. 19
  12. 66
  13. 2
  14. 4
  15. 5
  16. 39
  17. 4
  18. 594
  19. 5
  20. 111
  21. 6
  22. 19
  23. 8
  24. 5
  25. 42
  26. 69
  27. 33
  28. 3
  29. 85
  30. 3
  31. 5
  32. 5
  33. 21
  34. 8
  35. 408
  36. 36
  37. 10
  38. 77
  39. 297
  40. 13

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