                    ABCD
                    CABD
                    ACDB
                    DACB
                    BCDA
                    ACBD
                    ADCB
                    CDAB
                    DABC
                    BCAD
                    CADB
                    CDBA
                    CBAD
                    ABDC
                    ADBC
                    BDCA
                    DCBA
                    BACD
                    BADC
                    BDAC
                    CBDA
                    DBCA
                    DCAB

Listed above are   all-but-one   of the permutations of the symbols   A,   B,   C,   and   D,   except   for one permutation that's   not   listed.



Task

Find that missing permutation.



Methods

 Obvious method: 
        enumerate all permutations of   A,  B,  C,  and  D,  
        and then look for the missing permutation. 

 alternate method:
        Hint:  if all permutations were shown above,  how many 
        times would  A  appear in each position?     
        What is the  parity  of this number?

 another alternate method:
        Hint:  if you add up the letter values of each column, 
        does a missing letter   A,  B,  C,  and  D   from each
        column cause the total value for each column to be unique?



Related task

   Permutations)


BEGIN # find the missing permutation in a list using the XOR method of the Raku sample #
    # the list to find the missing permutation of #
    []STRING list = ( "ABCD", "CABD", "ACDB", "DACB", "BCDA"
                    , "ACBD", "ADCB", "CDAB", "DABC", "BCAD"
                    , "CADB", "CDBA", "CBAD", "ABDC", "ADBC"
                    , "BDCA", "DCBA", "BACD", "BADC", "BDAC"
                    , "CBDA", "DBCA", "DCAB"
                    );
    # sets b to b XOR v and returns b #
    PRIO XORAB = 1;
    OP   XORAB = ( REF BITS b, BITS v )REF BITS: b := b XOR v;
 
    # loop through each character of each element of the list #
    FOR c pos FROM LWB list[ LWB list ] TO UPB list[ LWB list ] DO
        # loop through each element of the list #
        BITS m := 16r0;
        FOR l pos FROM LWB list TO UPB list DO
            m XORAB BIN ABS list[ l pos ][ c pos ]
        OD;
        print( ( REPR ABS m ) )
    OD
END