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]

03 Dec 2003, 17:48

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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?

from China's site

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03 Dec 2003, 19:33

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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03 Dec 2003, 19:47

should this be calculated like this?

Total number = 25 x 26 x 25 = 16,250

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03 Dec 2003, 20:00

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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03 Dec 2003, 20:17

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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04 Dec 2003, 08:36

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]

17 May 2004, 18:26

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, 18:26

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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

use 26 character to make 3 characters password, only mid

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