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Number Puzzles Worksheet for Maths Olympiad

Maths Olympiad topic 25: Number puzzles and digit counting · Set 690 · 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 6? (a) 10 (b) 7 (c) 6 (d) 5
  2. 2.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) 41 (d) 32
  3. 3.A book has 172 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 409 (b) 399 (c) 408 (d) 344
  4. 4.How many times is the digit 7 written when you write all the numbers from 1 to 97? (a) 9 (b) 19 (c) 20 (d) 21
  5. 5.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) 6 (c) 21 (d) 18
  6. 6.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) 126 (c) 42 (d) 14
  7. 7.How many times is the digit 7 written when you write all the numbers from 1 to 81? (a) 17 (b) 18 (c) 8 (d) 19
  8. 8.How many times is the digit 3 written when you write all the numbers from 1 to 55? (a) 5 (b) 17 (c) 15 (d) 16
  9. 9.How many two-digit numbers have digits that add up to 3? (a) 4 (b) 3 (c) 10 (d) 2
  10. 10.How many times is the digit 8 written when you write all the numbers from 1 to 40? (a) 2 (b) 5 (c) 3 (d) 4
  11. 11.How many times is the digit 8 written when you write all the numbers from 1 to 52? (a) 6 (b) 5 (c) 4 (d) 3
  12. 12.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
  13. 13.How many times is the digit 4 written when you write all the numbers from 1 to 56? (a) 5 (b) 15 (c) 17 (d) 16
  14. 14.How many two-digit numbers have digits that add up to 5? (a) 10 (b) 4 (c) 5 (d) 6
  15. 15.The numbers 5 to 13 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) 30 (c) 81 (d) 9
  16. 16.How many times is the digit 9 written when you write all the numbers from 1 to 44? (a) 4 (b) 2 (c) 5 (d) 3
  17. 17.How many times is the digit 7 written when you write all the numbers from 1 to 31? (a) 4 (b) 3 (c) 2 (d) 1
  18. 18.How many times is the digit 9 written when you write all the numbers from 1 to 47? (a) 4 (b) 2 (c) 3 (d) 5
  19. 19.How many times is the digit 8 written when you write all the numbers from 1 to 60? (a) 6 (b) 4 (c) 5 (d) 7
  20. 20.A book has 213 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 522 (b) 426 (c) 531 (d) 532
  21. 21.How many two-digit numbers have digits that add up to 13? (a) 6 (b) 5 (c) 14 (d) 7
  22. 22.A book has 38 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 76 (b) 67 (c) 68 (d) 58
  23. 23.How many times is the digit 2 written when you write all the numbers from 1 to 81? (a) 18 (b) 8 (c) 17 (d) 19
  24. 24.How many times is the digit 6 written when you write all the numbers from 1 to 74? (a) 18 (b) 7 (c) 17 (d) 16
  25. 25.How many times is the digit 6 written when you write all the numbers from 1 to 97? (a) 19 (b) 20 (c) 9 (d) 21
  26. 26.How many two-digit numbers have digits that add up to 14? (a) 6 (b) 15 (c) 5 (d) 4
  27. 27.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) 63 (b) 24 (c) 7 (d) 21
  28. 28.How many times is the digit 7 written when you write all the numbers from 1 to 49? (a) 6 (b) 3 (c) 4 (d) 5
  29. 29.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) 90 (c) 10 (d) 30
  30. 30.A book has 195 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 477 (b) 468 (c) 390 (d) 478
  31. 31.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) 20 (b) 180 (c) 60 (d) 63
  32. 32.A book has 72 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 135 (b) 136 (c) 144 (d) 126
  33. 33.How many times is the digit 4 written when you write all the numbers from 1 to 59? (a) 15 (b) 5 (c) 16 (d) 17
  34. 34.How many two-digit numbers have digits that add up to 2? (a) 2 (b) 10 (c) 1 (d) 3
  35. 35.How many two-digit numbers have digits that add up to 4? (a) 3 (b) 10 (c) 5 (d) 4
  36. 36.A book has 26 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 34 (b) 44 (c) 43 (d) 52
  37. 37.How many times is the digit 4 written when you write all the numbers from 1 to 68? (a) 16 (b) 6 (c) 18 (d) 17
  38. 38.How many two-digit numbers have digits that add up to 15? (a) 5 (b) 3 (c) 4 (d) 16
  39. 39.How many times is the digit 8 written when you write all the numbers from 1 to 42? (a) 5 (b) 2 (c) 4 (d) 3
  40. 40.How many two-digit numbers have digits that add up to 7? (a) 10 (b) 8 (c) 6 (d) 7

Answer key

  1. 6
  2. 41
  3. 408
  4. 20
  5. 18
  6. 42
  7. 18
  8. 16
  9. 3
  10. 4
  11. 5
  12. 15
  13. 16
  14. 5
  15. 27
  16. 4
  17. 3
  18. 4
  19. 6
  20. 531
  21. 6
  22. 67
  23. 18
  24. 17
  25. 20
  26. 5
  27. 21
  28. 5
  29. 30
  30. 477
  31. 60
  32. 135
  33. 16
  34. 2
  35. 4
  36. 43
  37. 17
  38. 4
  39. 4
  40. 7

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