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 Solution to Christmas Puzzle 7.  CHRISTMAS GIFTS

Alice, Bob, Cathy and Dan gathered together to exchange Christmas presents.  Each of them brought two gifts.  Alice wrapped her gifts in green wrappers.  Bob wrapped his gifts in yellow wrappers.  Cathy wrapped her gifts in blue wrappers.  Dan wrapped his gifts in red wrappers.  They drew lots to determine which gifts they are supposed to receive. 

(1) Each of the receive two gifts in wrappers of  different colors,

(2) Each did not get the gifts they brought. 

(3) Alice did not receive any gift wrapped in yellow.  

(4) Cathy did not receive any gift wrapped in red. 

(5) Bob did not receive any gifts wrapped in Blue. 

From whom did Alice, Bob, Cathy and Dan each received gifts from?

Solution:

Set up a table as shown below:

  Green Yellow Blue Red
Alice X2 X3    
Bob   X2 X5  
Cathy     X2 X4
Dan       X2

Based on (2), cells marked X2 above can not happen.

Based on (3), (4), and (5), cells marked X3, X4, and X5 can not happen

The remaining cells on the table not marked X represent possible gifts received.  Since each received 2 gifts, therefore:

Alice received the Blue and Red Gifts.

Bob received the Green and Red Gifts.

Cathy received the Green and Yellow Gifts.

Since based on (1), there are only 2 Green gifts.  These belongs to Bob and Cathy.  Therefore, Dan did not received any Green Gift.

Therefore, Dan received the Blue and Yellow Gifts.

 

         

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Bits and Beyond...

Christmas is not a time nor a season, but a state of mind.  To cherish peace and goodwill, to be plenteous in mercy, is to have the real spirit of Christmas.

                             Calvin Coolidge

 

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