Six brothers Al, Bob, Cal, Don, Elmer and Fred always take the same seat when they have their meals in the circular dinner table. The following figure displays their seat numbers.

           1
      6       2
      5       3
          4


The following is known:

• Bob's seat number is precisely 1 larger than that of Elmer's seat number.
• The seat of Don is separated from Al's seat by precisely one of the other brothers.
• Al's seat number is either 1 larger than or 1 smaller than Fred's seat number.
• The absolute difference of Cal's seat number from that of Bob's and the absolute difference of Cal's seat number from that of Don's are respectively either, 2 and 5; or, 5 and 2.

Determine the respective seat numbers of the six brothers.

I used the following code

CLS 0
FOR a = 1 TO 6
 FOR b = 1 TO 6
  IF b <> a THEN
   FOR c = 1 TO 6
    IF c <> b AND c <> a THEN
     FOR d = 1 TO 6
      IF d <> a AND d <> b AND d <> c THEN
       FOR e = 1 TO 6
        IF e <> a AND e <> b AND e <> c AND e <> d THEN
         FOR f = 1 TO 6
          IF f <> a AND f <> b AND f <> c AND f <> d AND f <> e THEN
           IF b = e + 1 THEN
            IF ((d + 1) MOD 6) + 1 = a OR ((a + 1) MOD 6) + 1 = d THEN
             IF ABS(a - f) = 1 THEN
              IF (ABS(c - b) = 2 AND ABS(c - d) = 5) OR (ABS(c - b) = 5 AND ABS(c - d) = 2) THEN
               PRINT "Al is in seat " + STR$(a)
               PRINT "Bob is in seat " + STR$(b)
               PRINT "Cal is in seat " + STR$(c)
               PRINT "Don is in seat " + STR$(d)
               PRINT "Elmer is in seat " + STR$(e)
               PRINT "Fred is in seat " + STR$(f)
              END IF
             END IF
            END IF
           END IF
          END IF
         NEXT f
        END IF
       NEXT e
      END IF
     NEXT d
    END IF
   NEXT c
  END IF
 NEXT b
NEXT a

and got the following solution

Al is in seat  4
Bob is in seat  3
Cal is in seat  1
Don is in seat  6
Elmer is in seat  2
Fred is in seat  5

Posted by Daniel on 2009-05-25 14:35:08