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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 514 · 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.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) 21 (b) 63 (c) 24 (d) 7
  2. 2.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 10 (d) 8
  3. 3.How many times is the digit 4 written when you write all the numbers from 1 to 78? (a) 19 (b) 7 (c) 18 (d) 17
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 98? (a) 19 (b) 20 (c) 9 (d) 21
  5. 5.How many times is the digit 2 written when you write all the numbers from 1 to 34? (a) 13 (b) 14 (c) 3 (d) 15
  6. 6.A book has 129 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 279 (b) 280 (c) 270 (d) 258
  7. 7.How many times is the digit 4 written when you write all the numbers from 1 to 30? (a) 1 (b) 4 (c) 2 (d) 3
  8. 8.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 58 (c) 66 (d) 57
  9. 9.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) 77 (c) 68 (d) 78
  10. 10.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) 11 (d) 33
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 6 (b) 8 (c) 7 (d) 9
  12. 12.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 2 (c) 3 (d) 10
  13. 13.How many times is the digit 9 written when you write all the numbers from 1 to 55? (a) 4 (b) 6 (c) 5 (d) 3
  14. 14.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) 198 (c) 22 (d) 66
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 65? (a) 4 (b) 5 (c) 7 (d) 6
  16. 16.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) 30 (c) 9 (d) 81
  17. 17.A book has 21 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 24 (b) 34 (c) 42 (d) 33
  18. 18.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 5 (c) 4 (d) 3
  19. 19.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) 144 (b) 51 (c) 16 (d) 48
  20. 20.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 3 (c) 17 (d) 4
  21. 21.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) 17 (b) 51 (c) 54 (d) 153
  22. 22.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) 27 (d) 72
  23. 23.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) 180 (d) 20
  24. 24.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) 23 (b) 72 (c) 207 (d) 69
  25. 25.How many times is the digit 2 written when you write all the numbers from 1 to 95? (a) 9 (b) 21 (c) 20 (d) 19
  26. 26.A book has 177 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 354 (b) 424 (c) 423 (d) 414
  27. 27.How many times is the digit 5 written when you write all the numbers from 1 to 63? (a) 6 (b) 15 (c) 17 (d) 16
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 15 (b) 9 (c) 14 (d) 12
  29. 29.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 7 (d) 5
  30. 30.How many times is the digit 1 written when you write all the numbers from 1 to 97? (a) 9 (b) 20 (c) 21 (d) 19
  31. 31.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) 36 (b) 39 (c) 12 (d) 108
  32. 32.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 6 (c) 10 (d) 5
  33. 33.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 8 (d) 9
  34. 34.A book has 127 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 254 (b) 264 (c) 274 (d) 273
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 20 (d) 19
  36. 36.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  37. 37.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 7 (c) 10 (d) 5
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 38? (a) 2 (b) 4 (c) 1 (d) 3
  39. 39.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 18 (b) 20 (c) 9 (d) 19
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 1 (b) 4 (c) 2 (d) 3

Answer key

  1. 21
  2. 9
  3. 18
  4. 20
  5. 14
  6. 279
  7. 3
  8. 57
  9. 77
  10. 33
  11. 8
  12. 3
  13. 5
  14. 66
  15. 6
  16. 27
  17. 33
  18. 4
  19. 48
  20. 3
  21. 51
  22. 24
  23. 60
  24. 69
  25. 20
  26. 423
  27. 16
  28. 14
  29. 6
  30. 20
  31. 36
  32. 5
  33. 8
  34. 273
  35. 20
  36. 9
  37. 6
  38. 3
  39. 19
  40. 3

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