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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 365 · 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 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
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 38? (a) 13 (b) 3 (c) 14 (d) 15
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 47? (a) 3 (b) 6 (c) 5 (d) 4
  4. 4.A book has 137 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 303 (b) 304 (c) 274 (d) 294
  5. 5.A book has 34 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 59 (b) 60 (c) 50 (d) 68
  6. 6.How many times is the digit 4 written when you write all the numbers from 1 to 33? (a) 1 (b) 4 (c) 2 (d) 3
  7. 7.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  8. 8.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) 10 (b) 33 (c) 30 (d) 90
  9. 9.How many times is the digit 3 written when you write all the numbers from 1 to 86? (a) 8 (b) 19 (c) 18 (d) 20
  10. 10.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 7 (c) 8 (d) 6
  11. 11.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) 60 (b) 57 (c) 19 (d) 171
  12. 12.How many times is the digit 8 written when you write all the numbers from 1 to 54? (a) 6 (b) 3 (c) 4 (d) 5
  13. 13.How many times is the digit 6 written when you write all the numbers from 1 to 85? (a) 18 (b) 8 (c) 17 (d) 19
  14. 14.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) 153 (b) 17 (c) 54 (d) 51
  15. 15.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  16. 16.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 16 (b) 15 (c) 17 (d) 5
  17. 17.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) 7 (b) 24 (c) 21 (d) 63
  18. 18.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) 27 (b) 72 (c) 8 (d) 24
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 81? (a) 11 (b) 8 (c) 10 (d) 9
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 35? (a) 2 (b) 1 (c) 4 (d) 3
  21. 21.How many times is the digit 2 written when you write all the numbers from 1 to 37? (a) 15 (b) 13 (c) 14 (d) 3
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 43? (a) 4 (b) 16 (c) 15 (d) 14
  23. 23.How many times is the digit 8 written when you write all the numbers from 1 to 57? (a) 3 (b) 4 (c) 5 (d) 6
  24. 24.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) 11 (b) 33 (c) 99 (d) 36
  25. 25.A book has 99 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 189 (b) 180 (c) 190 (d) 198
  26. 26.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 17 (c) 3 (d) 4
  27. 27.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 1 (d) 2
  28. 28.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 5 (c) 4 (d) 6
  29. 29.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  30. 30.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) 159 (c) 160 (d) 150
  31. 31.How many times is the digit 4 written when you write all the numbers from 1 to 74? (a) 17 (b) 18 (c) 19 (d) 7
  32. 32.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 30 (b) 40 (c) 39 (d) 48
  33. 33.How many times is the digit 5 written when you write all the numbers from 1 to 49? (a) 4 (b) 5 (c) 6 (d) 3
  34. 34.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) 198 (b) 22 (c) 69 (d) 66
  35. 35.How many two-digit numbers have digits that add up to 11? (a) 12 (b) 9 (c) 7 (d) 8
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 87? (a) 19 (b) 18 (c) 20 (d) 8
  37. 37.A book has 176 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 411 (b) 420 (c) 352 (d) 421
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 94? (a) 9 (b) 20 (c) 21 (d) 19
  39. 39.How many times is the digit 7 written when you write all the numbers from 1 to 93? (a) 9 (b) 18 (c) 20 (d) 19
  40. 40.A book has 140 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 280 (b) 303 (c) 312 (d) 313

Answer key

  1. 18
  2. 14
  3. 5
  4. 303
  5. 59
  6. 3
  7. 2
  8. 30
  9. 19
  10. 7
  11. 57
  12. 5
  13. 18
  14. 51
  15. 3
  16. 16
  17. 21
  18. 24
  19. 10
  20. 3
  21. 14
  22. 15
  23. 5
  24. 33
  25. 189
  26. 3
  27. 2
  28. 5
  29. 4
  30. 159
  31. 18
  32. 39
  33. 5
  34. 66
  35. 8
  36. 19
  37. 420
  38. 20
  39. 19
  40. 312

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