perplexus.info :: Logic : The 8 cards

The 8 cards (Posted on 2009-01-31)

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.

Submitted by pcbouhid

Rating: 4.5000 (2 votes)

Solution: (Hide)

The white card #4 states that there are the same number of black cards before and after it. It follows:

.....b .... b ....#4(w)....b....b....

The white card #1 states that the next two cards are black. So, the black cards in one “side” are together and preceeded by white card #1. The options are:

1) .... #1(w) – b – b - ....#4(w)....b....b.... or

2)....b....b....#4(w)....#1(w) – b – b - ....

The black card #5 states that the previous card is of the same color as the next. All the black cards are positioned, so in case 1, the black card is one of the two at the right side, and in case 2, at the left side. We have the following options:

for case 1:
....#1(w) – b – b - ....#4(w)....#5(b)....b.... or
....#1(w) – b – b - ....#4(w).....b....#5(b)....

for case 2:
....#5(b)....b....#4(w)....#1(w) – b – b .... or
....b....#5(b)....#4(w)....#1(w) – b – b - ....

And since it states that the previous and the next card are of the same color, which is white, we have:

for case 1:
1) ....#1(w) – b – b - ....#4(w) - #5(b) – w - ....b....
2)#1(w) – b – b - #4(w) - w - #5(b) – w - b
3)#1(w) – b – b - #4(w) - b - w - #5(b) – w

for case 2:
1)w - #5(b) – w - b - #4(w) - #1(w) – b – b
2) ....b....w - #5(b) - #4(w)....#1(w) – b – b - ....
3)b - w - #5(b) – w - #4(w) - #1(w) – b – b.

Black card #7 states that the next two cards are of the same color, which is white. This is only possible in case 1.2 or in case 2.2. So we have:

case 1.2: #1(w) – b – #7(b) - #4(w) - w - #5(b) – w - b
case 2.2: w - #5(b) – w - #7(b) - #4(w) - #1(w) – b – b

Black card #8 states that the previous card is black. So the only possibility is case 2.2, and #8 is the last one:

w - #5(b) – w - #7(b) - #4(w) - #1(w) – #6(b) - #8(b)

Since white card #3 states that the previous card has the same color as the next:

#2(w) - #5(b) – #3(w) - #7(b) - #4(w) - #1(w) – #6(b) - #8(b).

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-06-10 00:16:58
re(3): No Subject	Charlie	2009-06-04 13:22:50
re(2): No Subject	varadarajan	2009-06-04 03:48:17
re: No Subject	Charlie	2009-06-03 12:24:51
No Subject	varadarajan	2009-06-03 11:47:40
re(3): Logical solution	pcbouhid	2009-02-01 16:47:11
re(2): Logical solution	Charlie	2009-02-01 14:26:52
re: Logical solution	pcbouhid	2009-02-01 08:02:20
Logical solution	Steve Herman	2009-01-31 22:48:42
computer solution	Charlie	2009-01-31 17:58:27

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