user
```
                    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)
assistant
(formerly Perl 6)

```
my @givens = <ABCD CABD ACDB DACB BCDA ACBD ADCB CDAB DABC BCAD CADB CDBA
                CBAD ABDC ADBC BDCA DCBA BACD BADC BDAC CBDA DBCA DCAB>;

my @perms = <A B C D>.permutations.map: *.join;

.say when none(@givens) for @perms;

```

Output:

```
DBAC
```

Of course, all of these solutions are working way too hard,
when you can just xor all the bits,
and the missing one will just pop right out:

```
say [~^] <ABCD CABD ACDB DACB BCDA ACBD ADCB CDAB DABC BCAD CADB CDBA
          CBAD ABDC ADBC BDCA DCBA BACD BADC BDAC CBDA DBCA DCAB>;

```

Output:

```
DBAC
```