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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 654 · 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 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) 90 (c) 30 (d) 10
  2. 2.A book has 109 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 220 (b) 210 (c) 219 (d) 218
  3. 3.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) 207 (c) 69 (d) 72
  4. 4.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) 27 (c) 8 (d) 24
  5. 5.How many times is the digit 6 written when you write all the numbers from 1 to 48? (a) 6 (b) 5 (c) 4 (d) 3
  6. 6.How many times is the digit 6 written when you write all the numbers from 1 to 39? (a) 5 (b) 3 (c) 4 (d) 2
  7. 7.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 339 (b) 304 (c) 349 (d) 348
  8. 8.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 5 (d) 10
  9. 9.How many times is the digit 4 written when you write all the numbers from 1 to 66? (a) 18 (b) 16 (c) 6 (d) 17
  10. 10.How many times is the digit 9 written when you write all the numbers from 1 to 59? (a) 5 (b) 4 (c) 6 (d) 7
  11. 11.How many times is the digit 9 written when you write all the numbers from 1 to 70? (a) 7 (b) 8 (c) 5 (d) 6
  12. 12.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 6 (d) 7
  13. 13.A book has 28 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 47 (c) 56 (d) 38
  14. 14.How many times is the digit 3 written when you write all the numbers from 1 to 62? (a) 15 (b) 17 (c) 16 (d) 6
  15. 15.How many times is the digit 3 written when you write all the numbers from 1 to 39? (a) 3 (b) 15 (c) 14 (d) 13
  16. 16.How many times is the digit 6 written when you write all the numbers from 1 to 96? (a) 21 (b) 19 (c) 20 (d) 9
  17. 17.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 5 (c) 6 (d) 4
  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) 21 (b) 189 (c) 63 (d) 66
  19. 19.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) 36 (b) 12 (c) 39 (d) 108
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 91? (a) 9 (b) 18 (c) 20 (d) 19
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 57? (a) 17 (b) 15 (c) 16 (d) 5
  22. 22.How many two-digit numbers have digits that add up to 17? (a) 18 (b) 3 (c) 2 (d) 1
  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 3 written when you write all the numbers from 1 to 84? (a) 8 (b) 19 (c) 20 (d) 18
  25. 25.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
  26. 26.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 9 (b) 19 (c) 20 (d) 21
  27. 27.How many times is the digit 2 written when you write all the numbers from 1 to 66? (a) 16 (b) 6 (c) 18 (d) 17
  28. 28.How many two-digit numbers have digits that add up to 6? (a) 7 (b) 5 (c) 6 (d) 10
  29. 29.A book has 44 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 80 (b) 70 (c) 79 (d) 88
  30. 30.A book has 148 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 296 (b) 337 (c) 336 (d) 327
  31. 31.How many two-digit numbers have digits that add up to 10? (a) 9 (b) 8 (c) 10 (d) 11
  32. 32.A book has 65 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 130 (b) 112 (c) 122 (d) 121
  33. 33.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) 16 (b) 144 (c) 51 (d) 48
  34. 34.How many times is the digit 7 written when you write all the numbers from 1 to 43? (a) 4 (b) 3 (c) 2 (d) 5
  35. 35.How many times is the digit 2 written when you write all the numbers from 1 to 70? (a) 7 (b) 18 (c) 16 (d) 17
  36. 36.A book has 202 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 489 (b) 498 (c) 404 (d) 499
  37. 37.A book has 85 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 152 (b) 170 (c) 162 (d) 161
  38. 38.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  39. 39.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 3 (d) 2
  40. 40.A book has 42 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 76 (c) 75 (d) 66

Answer key

  1. 30
  2. 219
  3. 69
  4. 24
  5. 5
  6. 4
  7. 348
  8. 4
  9. 17
  10. 6
  11. 7
  12. 7
  13. 47
  14. 16
  15. 14
  16. 20
  17. 5
  18. 63
  19. 36
  20. 19
  21. 16
  22. 2
  23. 21
  24. 19
  25. 18
  26. 20
  27. 17
  28. 6
  29. 79
  30. 336
  31. 9
  32. 121
  33. 48
  34. 4
  35. 17
  36. 498
  37. 161
  38. 4
  39. 2
  40. 75

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