When Kendra moved into her new house, four neighbors visited her with housewarming gifts. As she got to know them, Kendra realized that those who lived on the even side of the street – where house numbers are 2, 4, 6, 8 etc. – were the knights, who always spoke the truth while those who lived in the odd side – where house numbers are 1, 3, 5, 7 etc. – were the liars, who always spoke falsely.

The neighbor’s name, house number and the gifts are listed below, albeit not necessarily in that order:

Neighbor’s name: Bea, Celia, Daphne, Allison.
House numbers: #56,  #58,  #63,  #65
Gifts: cakes, salad, fruits, pilau.

Following are the statements made by each neighbor:

Bea
1. Celia lives in either #58 or #65.
2. Daphne does not live in either #56 or #65.

Celia
1. Bea and Daphne live on the same side of the street.
2. The woman who brought the salad does not live at #63 or #58.
3. Daphne does not live next door to me.

Daphne
1. I live in either #56 or #65.
2. Either Allison or Bea brought the fruits.

Allison
1. I live either at #63 or #56.
2. The woman who lives in #65 brought the pilau.

Given that Bea is a knight, use the above statements to find the house number and the gift of each neighbor.

We're told Bea is a knight. 

Combining Bea's second statement with Daphne's first statement, we know that Daphne is a liar. 

Combining this knowledge with Celia's first statement, we know that Celia is a liar, and thus Allison is the other knight. 

From there it's pretty straightforward. 

Bea lives at 58 and brought salad.

Celia lives at 65 and brought pilau.

Daphne lives at 63 and brought fruits.

Allison lives at 56 and brought cakes.

Posted by tomarken on 2014-02-25 14:25:15