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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 852 · 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 times is the digit 5 written when you write all the numbers from 1 to 60? (a) 15 (b) 16 (c) 17 (d) 6
  2. 2.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) 33 (c) 11 (d) 99
  3. 3.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) 19 (b) 60 (c) 57 (d) 171
  4. 4.How many times is the digit 9 written when you write all the numbers from 1 to 76? (a) 8 (b) 6 (c) 5 (d) 7
  5. 5.How many times is the digit 7 written when you write all the numbers from 1 to 51? (a) 5 (b) 6 (c) 4 (d) 3
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 50? (a) 16 (b) 15 (c) 5 (d) 14
  7. 7.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 6 (b) 9 (c) 7 (d) 8
  8. 8.How many times is the digit 6 written when you write all the numbers from 1 to 90? (a) 9 (b) 20 (c) 19 (d) 18
  9. 9.How many times is the digit 8 written when you write all the numbers from 1 to 35? (a) 4 (b) 1 (c) 2 (d) 3
  10. 10.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 10 (d) 2
  11. 11.How many times is the digit 3 written when you write all the numbers from 1 to 90? (a) 19 (b) 20 (c) 9 (d) 18
  12. 12.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 3 (c) 18 (d) 2
  13. 13.A book has 83 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 157 (b) 148 (c) 158 (d) 166
  14. 14.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 510 (b) 501 (c) 412 (d) 511
  15. 15.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 8 (c) 9 (d) 7
  16. 16.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) 42 (d) 126
  17. 17.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
  18. 18.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) 189 (b) 66 (c) 63 (d) 21
  19. 19.A book has 205 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 508 (b) 498 (c) 410 (d) 507
  20. 20.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
  21. 21.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 11 (c) 10 (d) 8
  22. 22.A book has 77 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 154 (b) 145 (c) 136 (d) 146
  23. 23.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) 48 (b) 16 (c) 144 (d) 51
  24. 24.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  25. 25.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 339 (c) 349 (d) 348
  26. 26.A book has 247 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 634 (b) 624 (c) 633 (d) 494
  27. 27.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) 21 (d) 6
  28. 28.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 88 (b) 79 (c) 70 (d) 80
  29. 29.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 176 (b) 168 (c) 158 (d) 167
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 30? (a) 4 (b) 3 (c) 1 (d) 2
  31. 31.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) 54 (c) 153 (d) 51
  32. 32.How many times is the digit 1 written when you write all the numbers from 1 to 61? (a) 16 (b) 6 (c) 18 (d) 17
  33. 33.How many times is the digit 2 written when you write all the numbers from 1 to 69? (a) 18 (b) 16 (c) 6 (d) 17
  34. 34.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 418 (b) 519 (c) 520 (d) 510
  35. 35.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 4 (b) 6 (c) 5 (d) 3
  36. 36.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) 90 (b) 30 (c) 10 (d) 33
  37. 37.How many times is the digit 1 written when you write all the numbers from 1 to 86? (a) 18 (b) 8 (c) 20 (d) 19
  38. 38.How many times is the digit 3 written when you write all the numbers from 1 to 60? (a) 16 (b) 17 (c) 15 (d) 6
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 11 (b) 13 (c) 5 (d) 12
  40. 40.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) 7 (c) 21 (d) 63

Answer key

  1. 16
  2. 33
  3. 57
  4. 7
  5. 5
  6. 15
  7. 8
  8. 19
  9. 3
  10. 2
  11. 19
  12. 2
  13. 157
  14. 510
  15. 8
  16. 42
  17. 39
  18. 63
  19. 507
  20. 69
  21. 9
  22. 145
  23. 48
  24. 5
  25. 348
  26. 633
  27. 18
  28. 79
  29. 167
  30. 3
  31. 51
  32. 17
  33. 17
  34. 519
  35. 5
  36. 30
  37. 19
  38. 16
  39. 12
  40. 21

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