maxThree.erl

-module(maxThree).
-export([maxThree/3]).

maxThree(X, X, X) ->
    X;

maxThree(X, X, Y) ->
    case max(X, Y) of
        X -> X;
        Y -> Y
    end;

maxThree(X, Y, X) ->
    case max(X, Y) of
        X -> X;
        Y -> Y
    end;

maxThree(Y, X, X) ->
    case max(X, Y) of
        X -> X;
        Y -> Y
    end;

maxThree(X, Y, Z) ->
    case max(X, Y) of
        X ->
            case max(X, Z) of
                X -> X;
                Z -> Z
            end;
        Y ->
            case max(Y, Z) of
                Y -> Y;
                Z -> Z
            end
    end.

Are the case statements necessary? These seemed to work, though they might fail for strange values.

maxThree(X,X,X) ->                                                                                                               
        X;                                                                                                                       
maxThree(X,X,Y) ->                                                                                                               
        max(X,Y);                                                                                                                
maxThree(X,Y,Y) ->                                                                                                               
        max(X,Y);                                                                                                                
maxThree(X,Y,Z) ->                                                                                                               
        max(max(X,Y),Z). 

Seems to work with order capable values:

83> one_fifteen:maxThree(a,b,c).       
c
84> one_fifteen:maxThree(c,a,b).
c
85> one_fifteen:maxThree("foo","bar","baz").
"foo"

@scull7, the first 3 patterns are not necessary as they are also covered by the last one.