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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 449 · 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 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) 54 (c) 17 (d) 51
  2. 2.How many two-digit numbers have digits that add up to 7? (a) 8 (b) 7 (c) 6 (d) 10
  3. 3.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) 19 (b) 171 (c) 60 (d) 57
  4. 4.A book has 242 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 484 (b) 609 (c) 618 (d) 619
  5. 5.How many times is the digit 5 written when you write all the numbers from 1 to 55? (a) 5 (b) 13 (c) 11 (d) 12
  6. 6.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  7. 7.How many times is the digit 1 written when you write all the numbers from 1 to 98? (a) 21 (b) 9 (c) 19 (d) 20
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 56? (a) 5 (b) 16 (c) 17 (d) 15
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 85? (a) 7 (b) 8 (c) 6 (d) 9
  10. 10.A book has 175 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 408 (b) 418 (c) 417 (d) 350
  11. 11.How many times is the digit 1 written when you write all the numbers from 1 to 99? (a) 20 (b) 19 (c) 9 (d) 21
  12. 12.How many two-digit numbers have digits that add up to 10? (a) 10 (b) 8 (c) 11 (d) 9
  13. 13.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 399 (b) 408 (c) 344 (d) 409
  14. 14.How many times is the digit 2 written when you write all the numbers from 1 to 97? (a) 20 (b) 21 (c) 19 (d) 9
  15. 15.A book has 184 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 445 (b) 368 (c) 444 (d) 435
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 37? (a) 4 (b) 2 (c) 1 (d) 3
  17. 17.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) 22 (b) 69 (c) 66 (d) 198
  18. 18.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 69 (b) 70 (c) 60 (d) 78
  19. 19.How many times is the digit 4 written when you write all the numbers from 1 to 92? (a) 9 (b) 20 (c) 19 (d) 18
  20. 20.How many times is the digit 2 written when you write all the numbers from 1 to 75? (a) 19 (b) 17 (c) 18 (d) 7
  21. 21.How many times is the digit 1 written when you write all the numbers from 1 to 82? (a) 8 (b) 18 (c) 20 (d) 19
  22. 22.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) 8 (b) 24 (c) 27 (d) 72
  23. 23.A book has 199 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 480 (c) 489 (d) 398
  24. 24.A book has 70 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 122 (b) 140 (c) 132 (d) 131
  25. 25.How many times is the digit 9 written when you write all the numbers from 1 to 49? (a) 3 (b) 5 (c) 4 (d) 6
  26. 26.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) 207 (b) 72 (c) 23 (d) 69
  27. 27.A book has 56 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 103 (b) 94 (c) 104 (d) 112
  28. 28.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) 162 (b) 18 (c) 57 (d) 54
  29. 29.A book has 33 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 66 (b) 57 (c) 48 (d) 58
  30. 30.How many two-digit numbers have digits that add up to 14? (a) 15 (b) 4 (c) 6 (d) 5
  31. 31.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 111 (b) 120 (c) 102 (d) 112
  32. 32.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 10 (d) 8
  33. 33.How many two-digit numbers have digits that add up to 17? (a) 1 (b) 2 (c) 3 (d) 18
  34. 34.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  35. 35.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) 5 (b) 18 (c) 45 (d) 15
  36. 36.How many times is the digit 7 written when you write all the numbers from 1 to 59? (a) 4 (b) 6 (c) 7 (d) 5
  37. 37.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 5 (c) 7 (d) 6
  38. 38.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) 45 (d) 42
  39. 39.How many times is the digit 9 written when you write all the numbers from 1 to 98? (a) 19 (b) 9 (c) 16 (d) 18
  40. 40.How many times is the digit 5 written when you write all the numbers from 1 to 30? (a) 1 (b) 2 (c) 3 (d) 4

Answer key

  1. 51
  2. 7
  3. 57
  4. 618
  5. 12
  6. 2
  7. 20
  8. 16
  9. 8
  10. 417
  11. 20
  12. 9
  13. 408
  14. 20
  15. 444
  16. 3
  17. 66
  18. 69
  19. 19
  20. 18
  21. 19
  22. 24
  23. 489
  24. 131
  25. 5
  26. 69
  27. 103
  28. 54
  29. 57
  30. 5
  31. 111
  32. 8
  33. 2
  34. 3
  35. 15
  36. 6
  37. 6
  38. 42
  39. 18
  40. 3

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