Six magicians A, B, C, D, E, F live in an island. Every Monday, the elders of the island rank the six magicians on their performance during the previous six days.

The rankings published on the previous Monday listed A 1st, B 2nd, C 3rd, D 4th, E 5th and F 6th.

This Monday’s ranking has each magician ranked in a different position than that of the previous Monday. We know that:

1. B’s change in ranking is greatest among the six magicians.

2. The product of D’s rankings for the two weeks is the same as the product of F’s rankings for the two weeks.

Determine the new rankings.

(In reply to solution by Charlie)

DECLARE SUB permute (a$)
CLS
a$ = "abcdef": h$ = a$
DO
  good = 1
  FOR i = 1 TO 6
    IF MID$(a$, i, 1) = MID$(h$, i, 1) THEN good = 0: EXIT FOR
  NEXT
  IF good THEN
    ac = ABS(INSTR(a$, "a") - INSTR(h$, "a"))
    bc = ABS(INSTR(a$, "b") - INSTR(h$, "b"))
    cc = ABS(INSTR(a$, "c") - INSTR(h$, "c"))
    dc = ABS(INSTR(a$, "d") - INSTR(h$, "d"))
    ec = ABS(INSTR(a$, "e") - INSTR(h$, "e"))
    fc = ABS(INSTR(a$, "f") - INSTR(h$, "f"))
    IF bc > ac AND bc > cc AND bc > dc AND bc > ec AND bc > fc THEN
      d = INSTR(a$, "d")
      f = INSTR(a$, "f")
      IF 6 * f = 4 * d THEN
         PRINT a$
      END IF
    END IF
  END IF
 
  permute a$
LOOP UNTIL a$ = h$

also produces

caefbd

Posted by Charlie on 2007-05-08 21:30:26