3-letter palindromes, math problem?

skitzo444 · #1 10-18-2007, 07:44 PM

You have three letters 26^3 combinations

how many palindromes are there in the 17,576 combinations

jstnrgrs · #2 10-18-2007, 08:01 PM

wouldn't it be 26^2?

skitzo444 · #3 10-18-2007, 08:25 PM

I thought it would be 26*25 because the first pick can be any letter, the second letter can be anything except the first pick (25/26) and the third letter can only be the same as the first (1/26).

(25/26)*(1/26) = 27.04
(26^3)/ 27.04 = 650

is there something i'm missing?

jay_shark · #4 10-18-2007, 08:31 PM

Suppose the middle letter is an A . Then the first and third letters may be any of {A,B,C,...Z} . There are 26 letters to choose . However the middle letter may be any of the 26 letters so it should be 26*26 = 676 .

skitzo444 · #5 10-18-2007, 08:32 PM

[ QUOTE ]
Suppose the middle letter is an A . Then the first and third letters may be any of {A,B,C,...Z} . There are 26 letters to choose . However the middle letter may be any of the 26 letters so it should be 26*26 = 676 .

[/ QUOTE ]

If the middle letter is A then the 1st and 3rd can be anything except A so there are 25 choices for the other letters.

tabako · #6 10-18-2007, 08:46 PM

AAA isn't a palindrome?

skitzo444 · #7 10-18-2007, 08:51 PM

[ QUOTE ]
AAA isn't a palindrome?

[/ QUOTE ]

No that's why theres only 25 choices for the 2nd letter because it excludes the first 1st letter that was picked...

tshort · #8 10-18-2007, 08:52 PM

[ QUOTE ]
[ QUOTE ]
AAA isn't a palindrome?

[/ QUOTE ]

No that's why theres only 25 choices for the 2nd letter because it excludes the first 1st letter that was picked...

[/ QUOTE ]

You seem to have an uncommon definition of a palindrome.

skitzo444 · #9 10-18-2007, 08:57 PM

Okay, I am trying to write a slot machine program in actionscript. I keep having trouble figuring out the expected value.

I want to have 1 top payout for a 1 in 17565 way such as ABC.
I then want to pay out a second tier for any Trips (AAA,BBB,CCC)
I then want it to pay for any palindrome (ABA, DFD)...but if the palindrome is all the same ie. FFF, then i want it to payout higher.

So, what would the expected value formula look like in this situation?

anisotropy · #10 10-18-2007, 09:51 PM

Would it not just be what jay posted above (26^2 = 676) minus all of the 'triples' (e.g. AAA, BBB, ...) of which there are 26 so the final total would be

676 - 26 = 650.