                    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)


list$ = "ABCD CABD ACDB DACB BCDA ACBD ADCB CDAB DABC BCAD CADB CDBA CBAD ABDC ADBC BDCA DCBA BACD BADC BDAC CBDA DBCA DCAB"
 
for a = asc("A") to asc("D")
  for b = asc("A") to asc("D")
    for c = asc("A") to asc("D")
      for d = asc("A") to asc("D")
        x$ = chr$(a) + chr$(b) + chr$(c)+ chr$(d)
        for i = 1 to 4                                            ' make sure each letter is unique
          j = instr(x$,mid$(x$,i,1))
          if instr(x$,mid$(x$,i,1),j + 1) <> 0 then goto [nxt]
        next i
       if instr(list$,x$) = 0 then print x$;" missing"            ' found missing permutation
[nxt] next d
    next c
  next b
next a