                    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)


void
paste(record r, index x, text p, integer a)
{
    p = insert(p, -1, a);
    x.delete(a);
    if (~x) {
        x.vcall(paste, -1, r, x, p);
    } else {
        r[p] = 0;
    }
    x[a] = 0;
}
 
integer
main(void)
{
    record r;
    list l;
    index x;
 
    l.bill(0, "ABCD", "CABD", "ACDB", "DACB", "BCDA", "ACBD", "ADCB",
           "CDAB", "DABC", "BCAD", "CADB", "CDBA", "CBAD", "ABDC", "ADBC",
           "BDCA", "DCBA", "BACD", "BADC", "BDAC", "CBDA", "DBCA", "DCAB");
 
    x['A'] = x['B'] = x['C'] = x['D'] = 0;
 
    x.vcall(paste, -1, r, x, "");
 
    l.ucall(r_delete, 1, r);
 
    o_(r.low, "\n");
 
    return 0;
}