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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 147 · 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 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) 171 (c) 19 (d) 60
  2. 2.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) 24 (b) 21 (c) 63 (d) 7
  3. 3.How many times is the digit 2 written when you write all the numbers from 1 to 90? (a) 19 (b) 18 (c) 9 (d) 20
  4. 4.How many times is the digit 1 written when you write all the numbers from 1 to 53? (a) 5 (b) 17 (c) 15 (d) 16
  5. 5.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  6. 6.A book has 76 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 134 (b) 144 (c) 152 (d) 143
  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) 42 (b) 45 (c) 126 (d) 14
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 94? (a) 9 (b) 15 (c) 12 (d) 14
  9. 9.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  10. 10.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) 21 (b) 63 (c) 189 (d) 66
  11. 11.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 3 (c) 1 (d) 18
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 5 (c) 4 (d) 10
  13. 13.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) 6 (b) 21 (c) 54 (d) 18
  14. 14.How many times is the digit 1 written when you write all the numbers from 1 to 67? (a) 6 (b) 17 (c) 16 (d) 18
  15. 15.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 9 (c) 8 (d) 7
  16. 16.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  17. 17.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) 72 (b) 24 (c) 8 (d) 27
  18. 18.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 70 (b) 88 (c) 80 (d) 79
  19. 19.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 376 (b) 447 (c) 456 (d) 457
  20. 20.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 5 (c) 16 (d) 3
  21. 21.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 166 (b) 148 (c) 157 (d) 158
  22. 22.How many times is the digit 9 written when you write all the numbers from 1 to 82? (a) 8 (b) 9 (c) 7 (d) 6
  23. 23.How many times is the digit 9 written when you write all the numbers from 1 to 74? (a) 6 (b) 5 (c) 8 (d) 7
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 41? (a) 5 (b) 3 (c) 2 (d) 4
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 35? (a) 2 (b) 4 (c) 1 (d) 3
  26. 26.How many two-digit numbers have digits that add up to 11? (a) 8 (b) 7 (c) 9 (d) 12
  27. 27.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) 54 (b) 57 (c) 162 (d) 18
  28. 28.How many times is the digit 8 written when you write all the numbers from 1 to 66? (a) 7 (b) 5 (c) 6 (d) 4
  29. 29.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 478 (b) 468 (c) 477 (d) 390
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 4 (d) 3
  31. 31.A book has 29 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 40 (b) 50 (c) 58 (d) 49
  32. 32.A book has 163 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 381 (b) 382 (c) 326 (d) 372
  33. 33.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 11 (c) 8 (d) 10
  34. 34.How many times is the digit 1 written when you write all the numbers from 1 to 63? (a) 18 (b) 16 (c) 6 (d) 17
  35. 35.How many times is the digit 6 written when you write all the numbers from 1 to 92? (a) 20 (b) 19 (c) 9 (d) 18
  36. 36.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 4 (b) 5 (c) 3 (d) 6
  37. 37.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) 99 (b) 36 (c) 33 (d) 11
  38. 38.How many times is the digit 5 written when you write all the numbers from 1 to 97? (a) 21 (b) 20 (c) 9 (d) 19
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 62? (a) 4 (b) 7 (c) 5 (d) 6
  40. 40.How many times is the digit 7 written when you write all the numbers from 1 to 33? (a) 2 (b) 1 (c) 4 (d) 3

Answer key

  1. 57
  2. 21
  3. 19
  4. 16
  5. 4
  6. 143
  7. 42
  8. 14
  9. 7
  10. 63
  11. 2
  12. 5
  13. 18
  14. 17
  15. 8
  16. 6
  17. 24
  18. 79
  19. 456
  20. 4
  21. 157
  22. 8
  23. 7
  24. 4
  25. 3
  26. 8
  27. 54
  28. 6
  29. 477
  30. 3
  31. 49
  32. 381
  33. 9
  34. 17
  35. 19
  36. 5
  37. 33
  38. 20
  39. 6
  40. 3

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