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Year 10 Computing — How strong a password is

Work out how many different passwords a rule allows, and use that count to say which of two rules is harder to guess your way through.

Name: ________________________

  1. 1.Sort each of these rules by how many different passwords it allows.

    Groups: Fewer than 1000 · More than 1000

    • 2 characters, each one of 30
    • 4 characters, each one of 7
    • 2 characters, each one of 45
    • 3 characters, each one of 11
    • 2 characters, each one of 12
    • 3 characters, each one of 9

  2. 2.A rule allows passwords of exactly 2 characters, and in each position it allows any of the 26 small letters and any of the 26 capital letters, and nothing else. How many passwords does the rule allow?

  3. 3.A password on one website is 3 characters long, and each character may be any of 20 letters. How many passwords does the website's rule allow?

  4. 4.One website's rule allows passwords 6 characters long, with 10 characters allowed in each position. Another website's rule allows passwords 4 characters long, with 30 characters allowed in each position. Which rule allows more passwords?

    • a) There is not enough here to tell
    • b) The rule with 6 characters and 10 choices
    • c) The two rules allow exactly the same number
    • d) The rule with 4 characters and 30 choices

  5. 5.A guessing machine gets through 200 passwords every second, and the rule it is working against allows 8400 different passwords. How many seconds does it need to try every one of them?

  6. 6.A rule allows 3 characters taken from a set of 20, and a guessing machine gets through 1000 passwords a second. How many seconds does the machine need before it has tried the lot?

  7. 7.A rule allows passwords of exactly 2 characters taken from a set of 30. It is changed to allow 4 characters, taken from that same set of 30. How many times more passwords does the new rule allow than the old one?

  8. 8.A rule allows passwords of 4 characters with 20 characters allowed in each position. It can be made stronger in one of two ways: one more character can be added to the length, or twenty more characters can be allowed in each position. Which change allows more passwords?

    • a) The two changes allow exactly the same number
    • b) Neither change makes any difference to the count
    • c) Allowing twenty more characters in each position
    • d) Adding one more character to the length

Answer key — Year 10 Computing — How strong a password is

  1. 1. 2 characters, each one of 12 → Fewer than 1000; 3 characters, each one of 9 → Fewer than 1000; 2 characters, each one of 30 → Fewer than 1000; 3 characters, each one of 11 → More than 1000; 4 characters, each one of 7 → More than 1000; 2 characters, each one of 45 → More than 1000
  2. 2. 2704
  3. 3. 8000
  4. 4. b) The rule with 6 characters and 10 choices
  5. 5. 42
  6. 6. 8
  7. 7. 900
  8. 8. d) Adding one more character to the length