Nine cards are disposed as shown:

           +---+---+---+
           | a | b | c |
           +---+---+---+
           | d | e | f |
           +---+---+---+
           | g | h | i |
           +---+---+---+

1) There are, at least, two Aces, two Kings, two Queens and two Jacks.
2) Every Ace borders a King and a Queen.
3) Every King borders a Queen and a Jack.
4) Every Queen borders a Jack.
Note: "border" means "touch" horizontally or vertically, not diagonally.

Identify the nine cards.

The first thing you notice is that Jack has no restrictions and so it must go in the middle

           +---+---+---+
           |   |   |   |
           +---+---+---+
           |   | J |   |
           +---+---+---+
           |   |   |   |
           +---+---+---+

Since every King must border a Jack both must touch this one

           +---+---+---+
           |   |   |   |
           +---+---+---+
           | K | J | K |
           +---+---+---+
           |   |   |   |
           +---+---+---+

Kings must also border Queens 

           +---+---+---+
           | Q |   | Q |
           +---+---+---+
           | K | J | K |
           +---+---+---+
           |   |   |   |
           +---+---+---+

This forces us to use another Jack since all Queens border Jacks

           +---+---+---+
           | Q | J | Q |
           +---+---+---+
           | K | J | K |
           +---+---+---+
           |   |   |   |
           +---+---+---+

The final row is easy since the two Aces must still be placed and they have to border K and Q

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

Posted by tanx on 2005-10-14 20:43:23