Logic
# Grid Puzzles

Four employees of a company Adam, Ben, Carl and David are planning on a $2$-week vacation for everyone. Their $4$ possible departure dates are March $22,$ March $29,$ April $5$ and April $12,$ and no two employees can leave on the same day. If the following rules determine the departure date for each with certainty, who is "X"?

$1.$ Adam does not leave the latest.

$2.$ Ben must not come back on April $12.$

$3.$ Carl leaves earlier than both Ben and David.

$4.$ Adam leaves a week after "X".

$7$ free movie tickets were available to the students in a college dorm. Amy, Beth, Cindy and Debra rushed to the management office and took all of the $7$ tickets. Since each of them talked to the office girl one-to-one, they did not know who actually got the tickets or how many, except for their own. So, they began talking among themselves.

Amy first asked Beth, "Did you get more tickets than I did?"

Beth answered, "I don't know."

Then Beth asked Cindy, "Did you get more tickets than I did?"

Cindy answered, "I don't know."

Upon hearing these, Debra said, "I now know the exact distribution of the $7$ tickets."

What is the distribution (Amy, Beth, Cindy, Debra) that Debra figured out?

Alex, Brian and Charles bought a dog, cat and fish. If Alex did not buy a dog and Charles did not buy a fish, what can we say about the animal that Brian bought?

$1.$ He could only have bought the dog or fish.

$2.$ He could have bought the dog, cat or fish.

$3.$ He bought the cat.

**Note:** Alex, Brian and Charles each bought one animal.