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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 54 · 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 8 written when you write all the numbers from 1 to 68? (a) 6 (b) 5 (c) 8 (d) 7
  2. 2.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) 45 (b) 15 (c) 48 (d) 135
  3. 3.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) 20 (c) 63 (d) 60
  4. 4.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) 216 (c) 72 (d) 24
  5. 5.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) 69 (b) 22 (c) 66 (d) 198
  6. 6.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
  7. 7.How many times is the digit 5 written when you write all the numbers from 1 to 42? (a) 3 (b) 4 (c) 5 (d) 2
  8. 8.How many times is the digit 9 written when you write all the numbers from 1 to 77? (a) 8 (b) 5 (c) 7 (d) 6
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 10 (c) 3 (d) 4
  10. 10.A book has 59 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 109 (b) 100 (c) 110 (d) 118
  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) 33 (c) 10 (d) 90
  12. 12.A book has 170 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 393 (b) 403 (c) 402 (d) 340
  13. 13.How many two-digit numbers have digits that add up to 4? (a) 5 (b) 3 (c) 4 (d) 10
  14. 14.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 14 (b) 12 (c) 13 (d) 5
  15. 15.How many times is the digit 9 written when you write all the numbers from 1 to 48? (a) 3 (b) 2 (c) 5 (d) 4
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 47? (a) 16 (b) 15 (c) 4 (d) 14
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 86? (a) 19 (b) 18 (c) 8 (d) 20
  18. 18.How many times is the digit 6 written when you write all the numbers from 1 to 88? (a) 8 (b) 19 (c) 18 (d) 20
  19. 19.How many times is the digit 9 written when you write all the numbers from 1 to 81? (a) 8 (b) 6 (c) 7 (d) 9
  20. 20.How many times is the digit 6 written when you write all the numbers from 1 to 83? (a) 17 (b) 19 (c) 18 (d) 8
  21. 21.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 14 (d) 6
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 38? (a) 2 (b) 3 (c) 5 (d) 4
  23. 23.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) 54 (b) 153 (c) 51 (d) 17
  24. 24.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 6 (c) 7 (d) 8
  25. 25.How many times is the digit 1 written when you write all the numbers from 1 to 31? (a) 14 (b) 3 (c) 15 (d) 13
  26. 26.How many times is the digit 4 written when you write all the numbers from 1 to 41? (a) 6 (b) 7 (c) 4 (d) 5
  27. 27.A book has 134 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 285 (b) 268 (c) 295 (d) 294
  28. 28.How many two-digit numbers have digits that add up to 12? (a) 7 (b) 8 (c) 6 (d) 13
  29. 29.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 618 (b) 619 (c) 484 (d) 609
  30. 30.A book has 149 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 330 (b) 298 (c) 339 (d) 340
  31. 31.A book has 181 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 426 (b) 362 (c) 436 (d) 435
  32. 32.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) 21 (b) 18 (c) 6 (d) 54
  33. 33.How many times is the digit 3 written when you write all the numbers from 1 to 84? (a) 8 (b) 19 (c) 18 (d) 20
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 3 (b) 6 (c) 4 (d) 5
  35. 35.How many times is the digit 5 written when you write all the numbers from 1 to 60? (a) 6 (b) 17 (c) 16 (d) 15
  36. 36.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 621 (b) 622 (c) 486 (d) 612
  37. 37.How many two-digit numbers have digits that add up to 5? (a) 4 (b) 10 (c) 5 (d) 6
  38. 38.How many times is the digit 9 written when you write all the numbers from 1 to 66? (a) 5 (b) 6 (c) 4 (d) 7
  39. 39.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) 126 (c) 42 (d) 45
  40. 40.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 9 (d) 11

Answer key

  1. 7
  2. 45
  3. 60
  4. 72
  5. 66
  6. 21
  7. 4
  8. 7
  9. 3
  10. 109
  11. 30
  12. 402
  13. 4
  14. 13
  15. 4
  16. 15
  17. 19
  18. 19
  19. 8
  20. 18
  21. 6
  22. 4
  23. 51
  24. 7
  25. 14
  26. 6
  27. 294
  28. 7
  29. 618
  30. 339
  31. 435
  32. 18
  33. 19
  34. 5
  35. 16
  36. 621
  37. 5
  38. 6
  39. 42
  40. 9

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