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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 238 · 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 6? (a) 6 (b) 7 (c) 10 (d) 5
  2. 2.A book has 57 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 105 (b) 114 (c) 106 (d) 96
  3. 3.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) 54 (c) 21 (d) 18
  4. 4.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 4 (b) 14 (c) 13 (d) 15
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 2 (b) 4 (c) 1 (d) 3
  6. 6.How many times is the digit 1 written when you write all the numbers from 1 to 30? (a) 13 (b) 12 (c) 14 (d) 3
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 3 (b) 15 (c) 13 (d) 14
  8. 8.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) 12 (b) 39 (c) 36 (d) 108
  9. 9.How many two-digit numbers have digits that add up to 4? (a) 10 (b) 4 (c) 3 (d) 5
  10. 10.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) 18 (b) 57 (c) 54 (d) 162
  11. 11.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) 30 (b) 10 (c) 33 (d) 90
  12. 12.How many times is the digit 3 written when you write all the numbers from 1 to 47? (a) 15 (b) 4 (c) 16 (d) 14
  13. 13.How many times is the digit 3 written when you write all the numbers from 1 to 63? (a) 6 (b) 17 (c) 16 (d) 18
  14. 14.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) 126 (b) 45 (c) 14 (d) 42
  15. 15.How many times is the digit 6 written when you write all the numbers from 1 to 64? (a) 6 (b) 11 (c) 12 (d) 9
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 35? (a) 11 (b) 9 (c) 3 (d) 10
  17. 17.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) 135 (c) 45 (d) 48
  18. 18.A book has 50 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 92 (b) 91 (c) 100 (d) 82
  19. 19.How many times is the digit 3 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 18 (d) 9
  20. 20.A book has 173 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 411 (c) 346 (d) 402
  21. 21.How many times is the digit 4 written when you write all the numbers from 1 to 75? (a) 19 (b) 7 (c) 17 (d) 18
  22. 22.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  23. 23.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
  24. 24.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) 180 (b) 60 (c) 20 (d) 63
  25. 25.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  26. 26.A book has 88 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 158 (b) 168 (c) 167 (d) 176
  27. 27.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) 9 (d) 27
  28. 28.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 10 (d) 6
  29. 29.A book has 95 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 182 (b) 172 (c) 181 (d) 190
  30. 30.How many two-digit numbers have digits that add up to 12? (a) 13 (b) 7 (c) 8 (d) 6
  31. 31.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 6 (c) 5 (d) 7
  32. 32.A book has 155 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 348 (b) 357 (c) 310 (d) 358
  33. 33.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 11 (c) 9 (d) 8
  34. 34.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) 18 (b) 5 (c) 15 (d) 45
  35. 35.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) 117 (b) 42 (c) 39 (d) 13
  36. 36.How many two-digit numbers have digits that add up to 8? (a) 10 (b) 7 (c) 9 (d) 8
  37. 37.How many times is the digit 8 written when you write all the numbers from 1 to 94? (a) 20 (b) 9 (c) 18 (d) 19
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 3 (b) 2 (c) 5 (d) 4
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 56? (a) 5 (b) 3 (c) 6 (d) 4
  40. 40.How many times is the digit 4 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 20 (d) 19

Answer key

  1. 6
  2. 105
  3. 18
  4. 14
  5. 3
  6. 13
  7. 14
  8. 36
  9. 4
  10. 54
  11. 30
  12. 15
  13. 17
  14. 42
  15. 11
  16. 10
  17. 45
  18. 91
  19. 19
  20. 411
  21. 18
  22. 3
  23. 177
  24. 60
  25. 9
  26. 167
  27. 27
  28. 5
  29. 181
  30. 7
  31. 6
  32. 357
  33. 9
  34. 15
  35. 39
  36. 8
  37. 19
  38. 4
  39. 5
  40. 20

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