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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 909 · 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 20 to 28 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 75 (b) 72 (c) 216 (d) 24
  2. 2.How many two-digit numbers have digits that add up to 5? (a) 6 (b) 4 (c) 10 (d) 5
  3. 3.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 6 (c) 5 (d) 15
  4. 4.How many times is the digit 3 written when you write all the numbers from 1 to 48? (a) 16 (b) 15 (c) 4 (d) 14
  5. 5.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
  6. 6.A book has 212 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 529 (b) 528 (c) 424 (d) 519
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 60? (a) 15 (b) 17 (c) 6 (d) 16
  8. 8.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  9. 9.How many times is the digit 5 written when you write all the numbers from 1 to 39? (a) 5 (b) 4 (c) 2 (d) 3
  10. 10.How many two-digit numbers have digits that add up to 17? (a) 3 (b) 1 (c) 18 (d) 2
  11. 11.A book has 69 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 138 (c) 120 (d) 129
  12. 12.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 2 (c) 1 (d) 3
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 20 (d) 18
  14. 14.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 2 (b) 3 (c) 4 (d) 5
  15. 15.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
  16. 16.A book has 93 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 178 (b) 186 (c) 177 (d) 168
  17. 17.A book has 45 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 72 (b) 90 (c) 82 (d) 81
  18. 18.How many times is the digit 8 written when you write all the numbers from 1 to 46? (a) 5 (b) 3 (c) 2 (d) 4
  19. 19.The numbers 1 to 9 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 5 (b) 18 (c) 45 (d) 15
  20. 20.How many times is the digit 9 written when you write all the numbers from 1 to 33? (a) 4 (b) 1 (c) 2 (d) 3
  21. 21.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) 33 (b) 30 (c) 90 (d) 10
  22. 22.How many two-digit numbers have digits that add up to 9? (a) 9 (b) 8 (c) 11 (d) 10
  23. 23.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) 63 (d) 21
  24. 24.How many times is the digit 9 written when you write all the numbers from 1 to 92? (a) 9 (b) 13 (c) 10 (d) 12
  25. 25.How many times is the digit 5 written when you write all the numbers from 1 to 82? (a) 19 (b) 8 (c) 18 (d) 17
  26. 26.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 4 (c) 3 (d) 10
  27. 27.A book has 31 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 44 (b) 62 (c) 53 (d) 54
  28. 28.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) 81 (b) 30 (c) 27 (d) 9
  29. 29.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 9 (d) 8
  30. 30.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 19 (b) 18 (c) 9 (d) 20
  31. 31.How many times is the digit 2 written when you write all the numbers from 1 to 54? (a) 15 (b) 16 (c) 5 (d) 17
  32. 32.How many times is the digit 6 written when you write all the numbers from 1 to 36? (a) 2 (b) 3 (c) 4 (d) 5
  33. 33.How many times is the digit 1 written when you write all the numbers from 1 to 78? (a) 7 (b) 18 (c) 17 (d) 19
  34. 34.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) 11 (c) 33 (d) 36
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 17 (b) 6 (c) 16 (d) 18
  36. 36.A book has 84 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 168 (b) 160 (c) 150 (d) 159
  37. 37.The numbers 11 to 19 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 15 (b) 48 (c) 135 (d) 45
  38. 38.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 172 (b) 182 (c) 190 (d) 181
  39. 39.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 207 (b) 217 (c) 324 (d) 216
  40. 40.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 15 (c) 4 (d) 16

Answer key

  1. 72
  2. 5
  3. 5
  4. 15
  5. 60
  6. 528
  7. 16
  8. 7
  9. 4
  10. 2
  11. 129
  12. 2
  13. 19
  14. 4
  15. 42
  16. 177
  17. 81
  18. 4
  19. 15
  20. 3
  21. 30
  22. 9
  23. 21
  24. 12
  25. 18
  26. 3
  27. 53
  28. 27
  29. 8
  30. 19
  31. 16
  32. 4
  33. 18
  34. 33
  35. 17
  36. 159
  37. 45
  38. 181
  39. 216
  40. 15

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