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use 26 character to make 3 characters password, only mid

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use 26 character to make 3 characters password, only mid [#permalink] New post 03 Dec 2003, 16:48
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use 26 character to make 3 characters password, only mid figure should be not tha same as the other two, ask number of password?


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 [#permalink] New post 03 Dec 2003, 18:33
Number of passwords without "middle character" rule:
26*26*26

then we have to subtract number of forbidden passwords :

char X char (char = X ( only one character or both of them) )

there are 26*3 passwords like those mentioned above,
each of characters (26 ) has three forbiden passwords...when X is at first place of the password , when X is at last place and when is X at both places.
e.g. Forbiden passwords for letter A:
A A char
char A A
A A A



Finally, number of possible passwords is :
26 * ( 26*26 - 3 ) = 17 498

:wink:
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 [#permalink] New post 03 Dec 2003, 18:47
should this be calculated like this?

Total number = 25 x 26 x 25 = 16,250
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 [#permalink] New post 03 Dec 2003, 19:00
I am not sure...where did I make mistake?
My way is indirect, your solution is direct and easier..but I am not sure now what is right answer...
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 [#permalink] New post 03 Dec 2003, 19:17
I got it...there are not only 26 x 3 forbidden passwords...
A A char - 25
char A A - 25
A A A -1
multiplied by 26 ..26 x ( 26+25).....=1326
Answer is 16250..
too complicated...
Well, it seems that I should go to sleep know...my brain doesn't work well anymore...it's 4 a.m. in my country :-D
Bye!
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 [#permalink] New post 04 Dec 2003, 07:36
my solution:

the total number is 26*26*26
the number of wrong combinations is 26*25*1

so, [26*26*26]–[26*25]=16926
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Re: PS [#permalink] New post 17 May 2004, 17:26
chihao wrote:
use 26 character to make 3 characters password, only mid figure should be not tha same as the other two, ask number of password?


Let XYZ be the password

case1: XYZ, where X and Z are the same.
26*25
case2: XYZ, where letters X and Z are different.
26*25*24

Answer = 26.25+26.25.24 = 26*25*25

OR:
Lets fix Y: this can be in 26 ways.
X and Z are different from Y: This can be done in 25*25 ways.

Answer = 26.25.25
Re: PS   [#permalink] 17 May 2004, 17:26
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use 26 character to make 3 characters password, only mid

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