                    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)


IncompleteList := "ABCD CABD ACDB DACB BCDA ACBD ADCB CDAB DABC BCAD CADB CDBA CBAD ABDC ADBC BDCA DCBA BACD BADC BDAC CBDA DBCA DCAB"
 
CompleteList := Perm( "ABCD" )
Missing := ""
 
Loop, Parse, CompleteList, `n, `r
  If !InStr( IncompleteList , A_LoopField )
    Missing .= "`n" A_LoopField
 
MsgBox Missing Permutation(s):%Missing%
 
;-------------------------------------------------
 
; Shortened version of [VxE]'s permutation function
; http://www.autohotkey.com/forum/post-322251.html#322251
Perm( s , dL="" , t="" , p="") {
   StringSplit, m, s, % d := SubStr(dL,1,1) , %t%
   IfEqual, m0, 1, return m1 d p
   Loop %m0%
   {
      r := m1
      Loop % m0-2
         x := A_Index + 1, r .= d m%x%
      L .= Perm(r, d, t, m%m0% d p)"`n" , mx := m1
      Loop % m0-1
         x := A_Index + 1, m%A_Index% := m%x%
      m%m0% := mx
   }
   return substr(L, 1, -1)
}