What is both possible and impossible at the same time?

Which flower has two lips?

Can it be possible to build a house that has all its four walls facing towards the South?

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

How many pluses should we put between the digits of 987654321 to get a total of 99, and where?

I am a ten letters word
The first four letters have the power to rule,
Next, four-letter can be eaten.
The next three-letter represents a lady.
I can fly as well

what am I looking for?

A cat had three kittens: Snophy, Topsy and Jorden. What was the mother's name?

Andrew sees a very rare bird named "Ruppell's vulture". Soon Andrew was dead. Can you explain the mystery, Mr. Sherlock?

In a stable, there are men and horses. In all, there are 22 heads and 72 feet. How many men and how many horses are in the stable