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I need a data validation formula to say, if status is "Registered" and ID is 6 characters long, the last character of the ID must be a letter.

I have managed to get this far but come to a brick wall;

AND( 
    ISPICKVAL( Referral_Status__c , 'Registered'), 
    LEN( Name ) = 6,
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I believe you could use a Regular Expression in validation. See this answer.

The RegEx could enforce both length requirement as well as the letter requirement on character 6 (along with other things, like if you wanted to check for only alphanumerics in the first 5).

For example:

boolean passes = Pattern.matches('^[\w]{5}[a-zA-Z]$');

or perhaps if you want a more explicit regex:

boolean passes = Pattern.matches('^[a-zA-Z_0-9]{5}[a-zA-Z]$');

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The Formula Operators and Functions documentation is a good resource here (albeit one that has a pretty abysmal UX).

There are several functions to get a substring, but probably the easiest one to use here given your description would be RIGHT(1) combined with REGEX() to test for an alphabetic character

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