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Seating Singularity (Posted on 2013-02-25) Difficulty: 3 of 5
Mr and Mrs Alden , Mr and Mrs Brent , Mr and Mrs Crown , Mr and Mrs Drake were seated around a table.

Their chairs were arranged around the square table like this:

                         a   b
                     +---+---+---+
                     |   |   |   |
                   h +---+---+---+ c
                     |   |   |   | 
                   g +---+---+---+ d
                     |   |   |   |  
                     +---+---+---+
                         f   e
                                          
For example, persons sitting at positions b and c are considered next to each other.
  1. The person sitting across from Mrs Alden was a man who sat on Mr Brent's immediate left.
  2. The person sitting on Mrs Crown's immediate left was a man who sat across from Mr Drake.
  3. Only one couple did not sit next to each other & this couple did not sit across from each other.
Which couple did not sit next to each other?

No Solution Yet Submitted by K Sengupta    
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Solution computer solution Comment 1 of 1

DECLARE FUNCTION opposite! (x!)
DECLARE SUB permute (a$)
CLS
a$ = "ABCDabcd": h$ = a$
DO
  MrsAlden = INSTR(a$, "a")
  tst = opposite(MrsAlden)
  MrBrent = tst - 1: IF MrBrent < 1 THEN MrBrent = MrBrent + 8
  IF MID$(a$, MrBrent, 1) = "B" AND MID$(a$, tst, 1) = UCASE$(MID$(a$, tst, 1)) THEN
    MrsCrown = INSTR(a$, "c")
    tst = MrsCrown + 1: IF tst > 8 THEN tst = tst - 8
    IF MID$(a$, tst, 1) = UCASE$(MID$(a$, tst, 1)) THEN
      MrDrake = opposite(tst)
      IF MID$(a$, MrDrake, 1) = "D" THEN
       IF LEFT$(a$, 2) < MID$(a$, 3, 2) THEN
       IF LEFT$(a$, 2) < MID$(a$, 5, 2) THEN
       IF LEFT$(a$, 2) < MID$(a$, 7, 2) THEN
           adjCt = 0: REDIM adj(4)
           MrAlden = INSTR(a$, "A")
           tst = ABS(MrAlden - MrsAlden)
           IF tst = 1 OR tst = 7 THEN adjCt = adjCt + 1: adj(1) = 1
           MrsBrent = INSTR(a$, "b")
           tst = ABS(MrBrent - MrsBrent)
           IF tst = 1 OR tst = 7 THEN adjCt = adjCt + 1: adj(2) = 1
           MrCrown = INSTR(a$, "C")
           tst = ABS(MrCrown - MrsCrown)
           IF tst = 1 OR tst = 7 THEN adjCt = adjCt + 1: adj(3) = 1
           MrsDrake = INSTR(a$, "d")
           tst = ABS(MrDrake - MrsDrake)
           IF tst = 1 OR tst = 7 THEN adjCt = adjCt + 1: adj(4) = 1
           IF adjCt = 3 THEN
             FOR i = 1 TO 4
              IF adj(i) = 0 THEN nonadj = i
             NEXT
             nadj$ = MID$("abcd", nonadj, 1)
             nadjpos = INSTR(a$, nadj$)
             opp = opposite(nadjpos)
             mate$ = MID$(a$, opp, 1)
             IF LCASE$(mate$) <> nadj$ THEN
               PRINT a$, nadj$: ct = ct + 1
             END IF
           END IF
       END IF
       END IF
       END IF
      END IF
    END IF
  END IF
  permute a$
LOOP UNTIL a$ = h$
PRINT ct

FUNCTION opposite (x)
  SELECT CASE x
    CASE 1
      opposite = 6
    CASE 2
      opposite = 5
    CASE 3
      opposite = 8
    CASE 4
      opposite = 7
    CASE 5
      opposite = 2
    CASE 6
      opposite = 1
    CASE 7
      opposite = 4
    CASE 8
      opposite = 3
  END SELECT
END FUNCTION

finds

positions
abcdefgh
--------
AabBCDdc      c

where capital letters are the men identified by last initial and women by lower-case letters.

So as not to include rotations, only the solution where the content of positions a and b is lower than the content of any other side of the table is shown.

Going clockwise as seen from above has the effect that being to someone's left means being to the right on the above scheme except when wrapping around the end to the beginning.

The letter to the right is the initial of the couple not sitting next to each other. Thus it is the Crowns who did not sit next to each other.


  Posted by Charlie on 2013-02-25 14:55:08
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