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The 8 cards (Posted on 2009-01-31) Difficulty: 2 of 5
You have 8 cards (pieces of paper) numbered from 1 to 8. The first 4 are all white, and the last 4 are all black. On each one is written:

#1: The next two cards are black.
#2: The next two cards are of different colors.
#3: The previous card has the same color as the next.
#4: There are the same number of black cards before and after this one.
#5: The previous card is of the same color as the next.
#6: The previous card is white.
#7: The next two cards are of the same color.
#8: The previous card is black.

Arrange the 8 cards in a row so that all the sentences result truthfully.

See The Solution Submitted by pcbouhid    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution | Comment 1 of 9

DECLARE SUB permute (a$)
 CLS
 numb$ = "12345678": numbH$ = numb$
 DO
  clr$ = ""
  FOR i = 1 TO 8
   IF MID$(numb$, i, 1) <= "4" THEN clr$ = clr$ + "w":  ELSE clr$ = clr$ + "b"
  NEXT
  ix = INSTR(numb$, "1"): v$ = MID$(clr$, ix, 3)
  IF v$ = "wbb" OR v$ = "bbb" THEN
    ix = INSTR(numb$, "2"): v$ = MID$(clr$, ix, 3)
    IF v$ = "wbw" OR v$ = "wwb" OR v$ = "bbw" OR v$ = "bwb" THEN

  ix = INSTR(numb$, "3")
  IF ix > 1 THEN
  v$ = MID$(clr$, ix - 1, 3)
  IF v$ = "bwb" OR v$ = "www" OR v$ = "bbb" OR v$ = "wbw" THEN
    ix = INSTR(numb$, "4"): bCt1 = 0: bCt2 = 0
    FOR iPos = 1 TO 8
     IF MID$(clr$, iPos, 1) = "b" THEN
       IF iPos < ix THEN bCt1 = bCt1 + 1
       IF iPos > ix THEN bCt2 = bCt2 + 1
     END IF
    NEXT iPos
    IF bCt1 = bCt2 THEN

  ix = INSTR(numb$, "5")
  IF ix > 1 THEN
  v$ = MID$(clr$, ix - 1, 3)
  IF v$ = "bbb" OR v$ = "wbw" OR v$ = "bwb" OR v$ = "www" THEN
    ix = INSTR(numb$, "6")
    IF ix > 1 THEN
    IF MID$(clr$, ix - 1, 2) = "wb" OR MID$(clr$, ix - 1, 2) = "ww" THEN

  ix = INSTR(numb$, "7")
  v$ = MID$(clr$, ix, 3)
  IF v$ = "bbb" OR v$ = "bww" OR v$ = "wbb" OR v$ = "www" THEN
    ix = INSTR(numb$, "8")
    IF ix > 1 THEN
    IF MID$(clr$, ix - 1, 2) = "bb" OR MID$(clr$, ix - 1, 2) = "bw" THEN
      PRINT : PRINT clr$: PRINT numb$: PRINT
    END IF
    END IF
  END IF

    END IF
    END IF
  END IF
  END IF

    END IF
  END IF
  END IF

    END IF
  END IF
  permute numb$
 LOOP UNTIL numb$ = numbH$

finds

wbwbwwbb
25374168

  Posted by Charlie on 2009-01-31 17:58:27
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