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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 753 · 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 6 written when you write all the numbers from 1 to 43? (a) 4 (b) 5 (c) 3 (d) 2
  2. 2.How many times is the digit 2 written when you write all the numbers from 1 to 78? (a) 19 (b) 17 (c) 7 (d) 18
  3. 3.How many times is the digit 5 written when you write all the numbers from 1 to 75? (a) 7 (b) 17 (c) 19 (d) 18
  4. 4.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) 63 (c) 7 (d) 24
  5. 5.A book has 30 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 60 (b) 42 (c) 51 (d) 52
  6. 6.A book has 218 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 436 (b) 546 (c) 547 (d) 537
  7. 7.A book has 209 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 519 (b) 418 (c) 520 (d) 510
  8. 8.How many two-digit numbers have digits that add up to 17? (a) 2 (b) 1 (c) 3 (d) 18
  9. 9.How many two-digit numbers have digits that add up to 5? (a) 5 (b) 4 (c) 6 (d) 10
  10. 10.How many times is the digit 5 written when you write all the numbers from 1 to 56? (a) 13 (b) 14 (c) 12 (d) 5
  11. 11.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) 48 (b) 15 (c) 135 (d) 45
  12. 12.A book has 224 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 564 (b) 448 (c) 565 (d) 555
  13. 13.How many two-digit numbers have digits that add up to 6? (a) 5 (b) 7 (c) 10 (d) 6
  14. 14.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) 339 (c) 340 (d) 298
  15. 15.How many times is the digit 8 written when you write all the numbers from 1 to 31? (a) 1 (b) 3 (c) 4 (d) 2
  16. 16.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 19 (b) 7 (c) 17 (d) 18
  17. 17.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) 72 (b) 207 (c) 69 (d) 23
  18. 18.How many two-digit numbers have digits that add up to 16? (a) 4 (b) 2 (c) 17 (d) 3
  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) 12 (b) 108 (c) 39 (d) 36
  20. 20.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) 117 (b) 39 (c) 13 (d) 42
  21. 21.How many two-digit numbers have digits that add up to 3? (a) 3 (b) 4 (c) 2 (d) 10
  22. 22.How many times is the digit 1 written when you write all the numbers from 1 to 91? (a) 20 (b) 19 (c) 9 (d) 21
  23. 23.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
  24. 24.How many times is the digit 8 written when you write all the numbers from 1 to 36? (a) 2 (b) 4 (c) 1 (d) 3
  25. 25.How many times is the digit 3 written when you write all the numbers from 1 to 98? (a) 20 (b) 21 (c) 19 (d) 9
  26. 26.How many times is the digit 5 written when you write all the numbers from 1 to 32? (a) 1 (b) 3 (c) 2 (d) 4
  27. 27.A book has 229 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 458 (b) 580 (c) 579 (d) 570
  28. 28.How many two-digit numbers have digits that add up to 13? (a) 7 (b) 6 (c) 14 (d) 5
  29. 29.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) 42 (c) 126 (d) 45
  30. 30.How many times is the digit 7 written when you write all the numbers from 1 to 48? (a) 5 (b) 3 (c) 4 (d) 6
  31. 31.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) 16 (c) 48 (d) 51
  32. 32.How many two-digit numbers have digits that add up to 9? (a) 8 (b) 9 (c) 11 (d) 10
  33. 33.How many two-digit numbers have digits that add up to 2? (a) 3 (b) 1 (c) 2 (d) 10
  34. 34.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 10 (c) 6 (d) 8
  35. 35.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) 66 (c) 21 (d) 189
  36. 36.How many two-digit numbers have digits that add up to 15? (a) 4 (b) 3 (c) 16 (d) 5
  37. 37.How many times is the digit 2 written when you write all the numbers from 1 to 49? (a) 14 (b) 4 (c) 16 (d) 15
  38. 38.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) 54 (c) 21 (d) 18
  39. 39.How many times is the digit 5 written when you write all the numbers from 1 to 69? (a) 18 (b) 6 (c) 17 (d) 16
  40. 40.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 3 (c) 5 (d) 10

Answer key

  1. 4
  2. 18
  3. 18
  4. 21
  5. 51
  6. 546
  7. 519
  8. 2
  9. 5
  10. 13
  11. 45
  12. 564
  13. 6
  14. 339
  15. 3
  16. 18
  17. 69
  18. 3
  19. 36
  20. 39
  21. 3
  22. 20
  23. 20
  24. 3
  25. 20
  26. 3
  27. 579
  28. 6
  29. 42
  30. 5
  31. 48
  32. 9
  33. 2
  34. 7
  35. 63
  36. 4
  37. 15
  38. 18
  39. 17
  40. 4

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