Eight cards are placed in the diagram shown below, one in each numbered cell. These are the facts:

a) There are 2 Aces, 2 Kings, 2 Queens and 2 Jacks.
b) Every Ace borders a King.
c) Every King borders a Queen.
d) Every Queen borders a Jack.
e) No Queen borders an Ace.
f) No two cards of the same kind border each other.

        +---+
        | 1 |
+---+---+---+
| 2 | 3 | 4 |
+---+---+---+---+
    | 5 | 6 | 7 |
    +---+---+---+
        | 8 |
        +---+

In what cells could you identify the card in it ?

My Explaination:

Firstly 6 has to be a King.
If 6 was a Jack then 7 & 8 can't be Jacks (Fact f), can't be Aces (Fact b) and can't be Kings (fact c) therefore 7 & 8 will be Queens. This can't be the case because now a King can't border a Queen (Fact c).
If 6 was a Queen then 4, 5, 7 & 8 can't be Queens (Fact f) or Aces (Fact e) so 4, 5, 7 & 8 must be Jacks and Kings and 1, 2 & 3 must be the other Queen and Aces but 2 & 3 can't be 2 Aces (Fact f) and can't be a Queen & Ace (Facts e)
If 6 was an Ace then a similar thing to it being a queen will exist so it can't be an Ace either. Therefore 6 must be a King.

If 6 is a King then 4, 5, 7 & 8 aren't Kings (Fact f). 7 & 8 can't be Queens (Fact d) so they must be either an Ace or Jack.

If 1 was an Ace then 4 would be a King (Fact b) but this can't exist as 4 & 6 can't both be Kings (Fact f). 1 is not an Ace.
If 1 was a Queen then 4 would be a Jack (Fact d) and then 5 would be a Queen so that the king in 6 borders a Queen (Fact c) and then 3 would be a Jack (Fact d) but then 3 & 4 are both Jack which can't exist (Fact f). 1 is not a Queen,
If 1 was a Jack then 4 could be a Queen or Ace. If 4 was an Ace then 7 & 8 would be the other Ace and other Jack. This can't exist as then no Queen could border a Jack (Fact d). 1 is not a Jack.
1 must therefore be the other King.

If 1 is a King then 4 is a Queen (Rule c). If 4 is a Queen 3 is a Jack (Rule d). 2 & 5 can't be Kings (Rule a) or Jacks (Rule f) so they must be Queen or Aces. 2 can't be an Ace (Rule b) so it must be a Queen. 5 must then be an Ace (Rule A).

7 & 8 are an Ace and a Jack but you cannot determine which is which.

1 - K
2 - Q
3 - J
4 - Q
5 - A
6 - K
7 - A or J
8 - A or J

You can identify cells 1 through to 6.

             +----+
              |  K  |
+----+---+----+
|  Q  |  J  |  Q  |
+----+---+----+----+
       |  A  |  K  | A/J |
       +---+----+----+
              | A/J |
             +----+

 

Edited on June 14, 2005, 1:33 pm

Edited on June 14, 2005, 1:42 pm

Edited on June 14, 2005, 1:44 pm

Posted by Lisa on 2005-06-14 13:29:45