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
(3) Alice did not receive any gift wrapped
(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
Set up a table as shown below:
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
Therefore, Dan received the Blue and Yellow Gifts.