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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 672 · 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 two-digit numbers have digits that add up to 13? (a) 7 (b) 5 (c) 6 (d) 14
  2. 2.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) 63 (b) 189 (c) 66 (d) 21
  3. 3.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) 45 (b) 42 (c) 126 (d) 14
  4. 4.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) 60 (c) 20 (d) 63
  5. 5.How many two-digit numbers have digits that add up to 14? (a) 4 (b) 5 (c) 15 (d) 6
  6. 6.How many times is the digit 7 written when you write all the numbers from 1 to 95? (a) 18 (b) 19 (c) 20 (d) 9
  7. 7.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 78 (c) 69 (d) 70
  8. 8.A book has 237 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 603 (b) 594 (c) 474 (d) 604
  9. 9.A book has 63 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 126 (b) 117 (c) 118 (d) 108
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 48? (a) 6 (b) 5 (c) 3 (d) 4
  11. 11.How many two-digit numbers have digits that add up to 2? (a) 1 (b) 3 (c) 10 (d) 2
  12. 12.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 10 (c) 4 (d) 6
  13. 13.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) 18 (b) 57 (c) 54 (d) 162
  14. 14.How many times is the digit 8 written when you write all the numbers from 1 to 83? (a) 13 (b) 12 (c) 8 (d) 10
  15. 15.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 4 (c) 10 (d) 5
  16. 16.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) 12 (b) 36 (c) 108 (d) 39
  17. 17.How many times is the digit 4 written when you write all the numbers from 1 to 88? (a) 18 (b) 19 (c) 8 (d) 20
  18. 18.A book has 60 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 120 (b) 112 (c) 111 (d) 102
  19. 19.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 6 (d) 5
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 94? (a) 9 (b) 21 (c) 20 (d) 19
  21. 21.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) 72 (d) 69
  22. 22.A book has 236 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 472 (b) 600 (c) 591 (d) 601
  23. 23.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) 48 (c) 144 (d) 51
  24. 24.How many times is the digit 4 written when you write all the numbers from 1 to 62? (a) 6 (b) 17 (c) 16 (d) 15
  25. 25.A book has 25 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 50 (b) 42 (c) 32 (d) 41
  26. 26.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) 45 (c) 15 (d) 18
  27. 27.A book has 245 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 490 (b) 628 (c) 618 (d) 627
  28. 28.The numbers 9 to 17 are placed in a 3 × 3 magic square, so every row, column and diagonal has the same sum. What is that sum? (a) 39 (b) 13 (c) 117 (d) 42
  29. 29.How many two-digit numbers have digits that add up to 15? (a) 3 (b) 16 (c) 5 (d) 4
  30. 30.How many times is the digit 2 written when you write all the numbers from 1 to 79? (a) 17 (b) 19 (c) 7 (d) 18
  31. 31.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) 90 (d) 30
  32. 32.A book has 206 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 412 (b) 501 (c) 511 (d) 510
  33. 33.A book has 243 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 622 (b) 486 (c) 621 (d) 612
  34. 34.How many times is the digit 2 written when you write all the numbers from 1 to 41? (a) 13 (b) 4 (c) 14 (d) 15
  35. 35.How many two-digit numbers have digits that add up to 9? (a) 11 (b) 10 (c) 8 (d) 9
  36. 36.How many times is the digit 3 written when you write all the numbers from 1 to 43? (a) 4 (b) 14 (c) 15 (d) 16
  37. 37.A book has 146 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 331 (b) 330 (c) 321 (d) 292
  38. 38.A book has 54 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 108 (b) 90 (c) 100 (d) 99
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 92? (a) 9 (b) 20 (c) 18 (d) 19
  40. 40.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) 21 (b) 24 (c) 7 (d) 63

Answer key

  1. 6
  2. 63
  3. 42
  4. 60
  5. 5
  6. 19
  7. 69
  8. 603
  9. 117
  10. 5
  11. 2
  12. 5
  13. 54
  14. 12
  15. 4
  16. 36
  17. 19
  18. 111
  19. 6
  20. 20
  21. 69
  22. 600
  23. 48
  24. 16
  25. 41
  26. 15
  27. 627
  28. 39
  29. 4
  30. 18
  31. 30
  32. 510
  33. 621
  34. 14
  35. 9
  36. 15
  37. 330
  38. 99
  39. 19
  40. 21

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