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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 799 · 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.A book has 152 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 304 (b) 339 (c) 349 (d) 348
  2. 2.A book has 187 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 454 (b) 374 (c) 453 (d) 444
  3. 3.A book has 51 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 84 (b) 93 (c) 94 (d) 102
  4. 4.How many two-digit numbers have digits that add up to 15? (a) 16 (b) 5 (c) 3 (d) 4
  5. 5.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) 8 (c) 72 (d) 24
  6. 6.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) 144 (b) 48 (c) 51 (d) 16
  7. 7.How many times is the digit 2 written when you write all the numbers from 1 to 82? (a) 8 (b) 19 (c) 20 (d) 18
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 6 (b) 10 (c) 5 (d) 7
  9. 9.A book has 32 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 64 (b) 56 (c) 55 (d) 46
  10. 10.A book has 103 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 206 (b) 192 (c) 202 (d) 201
  11. 11.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 17 (b) 19 (c) 18 (d) 8
  12. 12.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 4 (b) 3 (c) 5 (d) 2
  13. 13.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) 66 (b) 69 (c) 198 (d) 22
  14. 14.How many times is the digit 4 written when you write all the numbers from 1 to 35? (a) 3 (b) 4 (c) 2 (d) 5
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 78? (a) 8 (b) 9 (c) 6 (d) 7
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 83? (a) 7 (b) 6 (c) 8 (d) 9
  17. 17.A book has 24 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 48 (b) 40 (c) 39 (d) 30
  18. 18.A book has 197 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 394 (c) 474 (d) 483
  19. 19.How many two-digit numbers have digits that add up to 12? (a) 8 (b) 6 (c) 13 (d) 7
  20. 20.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
  21. 21.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 350 (b) 418 (c) 417 (d) 408
  22. 22.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) 36 (c) 33 (d) 11
  23. 23.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 609 (b) 618 (c) 619 (d) 484
  24. 24.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) 30 (c) 90 (d) 33
  25. 25.How many times is the digit 8 written when you write all the numbers from 1 to 59? (a) 6 (b) 5 (c) 7 (d) 4
  26. 26.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) 108 (b) 36 (c) 39 (d) 12
  27. 27.How many times is the digit 1 written when you write all the numbers from 1 to 41? (a) 14 (b) 4 (c) 15 (d) 16
  28. 28.How many times is the digit 9 written when you write all the numbers from 1 to 31? (a) 4 (b) 2 (c) 1 (d) 3
  29. 29.How many times is the digit 1 written when you write all the numbers from 1 to 55? (a) 5 (b) 17 (c) 15 (d) 16
  30. 30.How many times is the digit 6 written when you write all the numbers from 1 to 52? (a) 4 (b) 6 (c) 5 (d) 3
  31. 31.How many times is the digit 1 written when you write all the numbers from 1 to 56? (a) 16 (b) 17 (c) 5 (d) 15
  32. 32.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) 66 (b) 189 (c) 21 (d) 63
  33. 33.How many times is the digit 8 written when you write all the numbers from 1 to 58? (a) 4 (b) 6 (c) 5 (d) 7
  34. 34.How many times is the digit 6 written when you write all the numbers from 1 to 77? (a) 18 (b) 17 (c) 7 (d) 19
  35. 35.How many times is the digit 1 written when you write all the numbers from 1 to 50? (a) 14 (b) 16 (c) 15 (d) 5
  36. 36.How many two-digit numbers have digits that add up to 3? (a) 10 (b) 4 (c) 3 (d) 2
  37. 37.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 10 (c) 7 (d) 6
  38. 38.How many two-digit numbers have digits that add up to 9? (a) 10 (b) 11 (c) 8 (d) 9
  39. 39.How many two-digit numbers have digits that add up to 11? (a) 7 (b) 12 (c) 8 (d) 9
  40. 40.How many times is the digit 6 written when you write all the numbers from 1 to 44? (a) 4 (b) 5 (c) 3 (d) 2

Answer key

  1. 348
  2. 453
  3. 93
  4. 4
  5. 24
  6. 48
  7. 19
  8. 6
  9. 55
  10. 201
  11. 18
  12. 4
  13. 66
  14. 4
  15. 8
  16. 8
  17. 39
  18. 483
  19. 7
  20. 4
  21. 417
  22. 33
  23. 618
  24. 30
  25. 6
  26. 36
  27. 15
  28. 3
  29. 16
  30. 5
  31. 16
  32. 63
  33. 6
  34. 18
  35. 15
  36. 3
  37. 7
  38. 9
  39. 8
  40. 4

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