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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 203 · 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 41? (a) 3 (b) 5 (c) 4 (d) 2
  2. 2.How many two-digit numbers have digits that add up to 2? (a) 10 (b) 1 (c) 2 (d) 3
  3. 3.How many two-digit numbers have digits that add up to 16? (a) 2 (b) 4 (c) 3 (d) 17
  4. 4.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) 51 (b) 16 (c) 144 (d) 48
  5. 5.How many times is the digit 4 written when you write all the numbers from 1 to 58? (a) 5 (b) 16 (c) 17 (d) 15
  6. 6.How many times is the digit 8 written when you write all the numbers from 1 to 84? (a) 8 (b) 11 (c) 13 (d) 14
  7. 7.How many two-digit numbers have digits that add up to 14? (a) 5 (b) 6 (c) 15 (d) 4
  8. 8.How many two-digit numbers have digits that add up to 6? (a) 10 (b) 7 (c) 5 (d) 6
  9. 9.How many times is the digit 9 written when you write all the numbers from 1 to 63? (a) 4 (b) 6 (c) 7 (d) 5
  10. 10.How many times is the digit 6 written when you write all the numbers from 1 to 76? (a) 7 (b) 19 (c) 18 (d) 17
  11. 11.How many two-digit numbers have digits that add up to 3? (a) 2 (b) 3 (c) 10 (d) 4
  12. 12.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) 57 (c) 54 (d) 18
  13. 13.How many times is the digit 8 written when you write all the numbers from 1 to 71? (a) 8 (b) 5 (c) 7 (d) 6
  14. 14.A book has 208 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 507 (b) 516 (c) 416 (d) 517
  15. 15.How many times is the digit 7 written when you write all the numbers from 1 to 32? (a) 2 (b) 1 (c) 4 (d) 3
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 39? (a) 2 (b) 3 (c) 4 (d) 5
  17. 17.How many two-digit numbers have digits that add up to 13? (a) 14 (b) 7 (c) 6 (d) 5
  18. 18.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) 33 (b) 10 (c) 30 (d) 90
  19. 19.A book has 158 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 357 (b) 316 (c) 366 (d) 367
  20. 20.How many times is the digit 1 written when you write all the numbers from 1 to 76? (a) 7 (b) 17 (c) 18 (d) 19
  21. 21.A book has 222 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 559 (b) 444 (c) 549 (d) 558
  22. 22.How many times is the digit 4 written when you write all the numbers from 1 to 47? (a) 14 (b) 4 (c) 13 (d) 12
  23. 23.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 4 (d) 5
  24. 24.A book has 223 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 561 (b) 562 (c) 446 (d) 552
  25. 25.How many two-digit numbers have digits that add up to 7? (a) 7 (b) 8 (c) 6 (d) 10
  26. 26.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) 51 (b) 54 (c) 153 (d) 17
  27. 27.How many two-digit numbers have digits that add up to 10? (a) 11 (b) 9 (c) 8 (d) 10
  28. 28.How many times is the digit 5 written when you write all the numbers from 1 to 62? (a) 15 (b) 16 (c) 17 (d) 6
  29. 29.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) 54 (b) 18 (c) 6 (d) 21
  30. 30.A book has 67 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 116 (b) 126 (c) 125 (d) 134
  31. 31.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) 189 (b) 66 (c) 21 (d) 63
  32. 32.How many times is the digit 2 written when you write all the numbers from 1 to 42? (a) 15 (b) 14 (c) 4 (d) 16
  33. 33.A book has 39 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 78 (b) 70 (c) 69 (d) 60
  34. 34.A book has 188 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 456 (b) 447 (c) 376 (d) 457
  35. 35.A book has 233 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 582 (b) 466 (c) 591 (d) 592
  36. 36.How many times is the digit 8 written when you write all the numbers from 1 to 69? (a) 5 (b) 6 (c) 8 (d) 7
  37. 37.How many times is the digit 9 written when you write all the numbers from 1 to 42? (a) 3 (b) 5 (c) 2 (d) 4
  38. 38.How many times is the digit 4 written when you write all the numbers from 1 to 83? (a) 8 (b) 18 (c) 19 (d) 17
  39. 39.How many two-digit numbers have digits that add up to 8? (a) 7 (b) 9 (c) 8 (d) 10
  40. 40.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 6 (c) 5 (d) 4

Answer key

  1. 4
  2. 2
  3. 3
  4. 48
  5. 16
  6. 13
  7. 5
  8. 6
  9. 6
  10. 18
  11. 3
  12. 54
  13. 7
  14. 516
  15. 3
  16. 4
  17. 6
  18. 30
  19. 366
  20. 18
  21. 558
  22. 13
  23. 4
  24. 561
  25. 7
  26. 51
  27. 9
  28. 16
  29. 18
  30. 125
  31. 63
  32. 15
  33. 69
  34. 456
  35. 591
  36. 7
  37. 4
  38. 18
  39. 8
  40. 5

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