                    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)


V perms = [‘ABCD’, ‘CABD’, ‘ACDB’, ‘DACB’, ‘BCDA’, ‘ACBD’, ‘ADCB’, ‘CDAB’,
           ‘DABC’, ‘BCAD’, ‘CADB’, ‘CDBA’, ‘CBAD’, ‘ABDC’, ‘ADBC’, ‘BDCA’,
           ‘DCBA’, ‘BACD’, ‘BADC’, ‘BDAC’, ‘CBDA’, ‘DBCA’, ‘DCAB’]
 
V missing = ‘’
L(i) 4
   V cnt = [0] * 4
   L(j) 0 .< perms.len
      cnt[perms[j][i].code - ‘A’.code]++
   L(j) 4
      I cnt[j] != factorial(4-1)
         missing ‘’= Char(code' ‘A’.code + j)
         L.break
 
print(missing)