Four pairs of lords and ladies all went to a royal ball. Each lord was wearing one color (yellow, red, blue, or green) and each lady was also wearing one of these colors. No couple was wearing the same color, so it was hard to tell who was married to who.

Using the clues, can you determine which lord is with which lady?

1. The Green Lord is with the Red Lady, if and only if the Yellow Lord is with the Blue Lady.

2. The Yellow Lord is with the Red Lady if and only if the Green Lord is with the Yellow Lady

3. The Red Lord is with the Blue Lady, if and only if the Green Lord is with the Red Lady.

Looking at the first and last clues, there is a contradiction.  If the Red lord is with the Blue lady, then the Green lord is with the Red lady, then the Yellow lord is with the Blue lady.  Since this does not work out, none of those pairs can match up.

Notice that neither the Yellow, nor the Red lords can match up with the Blue lady (not to mention the Blue lord).  Therefore, the Green lord is with the Blue lady, and the conditions in statement 2 are false.

To match up the rest, the Yellow lord can't be with the Red Lady, Blue Lady, nor the Yellow lady.  Therefore, the Yellow lord was with the Green lady.  The Red lord then matches with the Yellow lady, and the Blue lord with the Red lady.

To sum this all up:

Lord      Lady
Green     Blue
Yellow    Green
Red        Yellow
Blue       Red

Posted by Tristan on 2004-04-25 12:01:33