## cinar 3 years ago password question, need some help..

1. cinar

2. lopus
3. wio

a) Let's try first by calculating the total number of passwords without requirements, and then subtracting the total number of passwords which DON'T meet the requirements.

4. wio

Cinar, can you do this?

5. cinar

62^10

6. cinar

that is total only..

7. wio

Now how many don't meet the 'at least one digit' rule, how many don't meet the 'at least one lower case letter', and how many don't meet the 'at least one upper case letter' requirement?

8. cinar

10^52+10^36+10^36

9. cinar

listen I'll be right back ok, give me couple minutes, I need to do something..

10. wio

\( (26 +26)^{10}\) Have no digit \( (26+10)^{10} \) Have no lower case \((26+10)^{10} \) Have no upper case

11. wio

We still double count the ones who break two or more rules, so we have to get rid of them. \(10^{10} \) break both upper and lower case rule \(26^{10} \) break both upper case and digit rule \(26^{10} \) break both lower case and digit rule \(0\) break all three rules, because it must contain at least a digit or letter

12. cinar

you'are right, I made a typo..

13. wio

So we have \((10+26+26)^{10} - ((10+26)^{10} + (10+26)^{10} + (26+26)^{10} - (10^{10} + 26^{10} + 26^{10})) \)

14. wio

Do you understand how I did that?

15. cinar

hold on..

16. cinar

it is like union of three set..

17. wio

Yeah

18. wio

Are you doing probability with set theory?

19. wio

Discreet math?

20. cinar

Discreet math

21. wio

So do you or don't you understand how I got what I got?

22. cinar

so, AUBUC=A+B+C-AIB-AIC-BIC+AIBIC I=intersection

23. wio

Yeah

24. cinar

got it..

25. cinar

how about part b, any idea..

26. wio

Do you have any ideas where to start?

27. cinar

let see

28. cinar

preceded by a letter means a1 or 1a

29. cinar

I am confused..

30. wio

I'm pretty sure it means a1

31. cinar

hmm, then password cannot be begun by a number..

32. wio

Well, one thing to ask is, must all digits be preceded by a number, or just at least one digit?

33. cinar

and also no number is successive

34. cinar

22 or 555 not allowed

35. cinar

a2ddd3y8jj8i898 is ok

36. wio

I think a123456789 is also okay, because it has one digit immediately preceded by a letter. They didn't say ALL must follow the rule, just one.

37. wio

so 1a23456789 would be ok too.

38. cinar

that' why I am confused..

39. cinar

listen I need some break to eat something..

40. cinar

I am back..

41. wio

Ok. So one thing we can take into consideration is that for a password to have a digit and be invalid, it would have to have to be 1... 11.... 111.... basically a bunch of digits in order with no letters in between.

42. wio

So one way is 1 digit and then 9 letters, with at least one capital and one lowercase

43. wio

So find how many ways we can have a password that is valid in (a) and not valid in (b) and subtract that from (a)