                    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)


 
PROGRAM MISSING
 
CONST N=4
 
DIM PERMS$[23]
 
BEGIN
  PRINT(CHR$(12);) ! CLS
  DATA("ABCD","CABD","ACDB","DACB","BCDA","ACBD","ADCB")
  DATA("CDAB","DABC","BCAD","CADB","CDBA","CBAD","ABDC","ADBC")
  DATA("BDCA","DCBA","BACD","BADC","BDAC","CBDA","DBCA","DCAB")
 
  FOR I%=1 TO UBOUND(PERMS$,1) DO
    READ(PERMS$[I%])
  END FOR
 
  SOL$="...."
 
  FOR I%=1 TO N DO
    CH$=CHR$(I%+64)
    COUNT%=0
    FOR Z%=1 TO N DO
       COUNT%=0
       FOR J%=1 TO UBOUND(PERMS$,1) DO
          IF CH$=MID$(PERMS$[J%],Z%,1) THEN COUNT%=COUNT%+1 END IF
       END FOR
       IF COUNT%<>6 THEN
           !$RCODE="MID$(SOL$,Z%,1)=CH$"
       END IF
    END FOR
  END FOR
  PRINT("Solution is: ";SOL$)
END PROGRAM
 