Dia. 1. Correct
Dia. 1. The hane tesuji
Black must first play the hane of 1, then connect with 3. White is forced to rescue his two marked stones with 2 and 4. As a result of this exchange, Black has become strong on the outside. Now he can shift his attention to the two white stones at the bottom.

Dia. 2 The nose-attachment.
Dia. 2. The nose-attachment tesuji.
Black starts his attack with the nose-attachment tesuji of 5. For the go player who is familiar with this tesuji, it would be the move that would stand out above all others. However, without the preparatory moves of 1 and 3 in Dia. 1, it would come to nought.

If White tries to escape with 6 —

Dia. 3. The net tesuji.
Dia. 3. The net tesuji.
Black follows up with the net tesuji (geta) of 7. White now has no way to escape.

Dia. 4.No escape 1
Dia. 4. No escape 1
White tries to escape by cutting through with 8 and 10, then follows up with another atari at 12. Black simply extends to 13. The only atari that White now has left is 14. However, after 15, White has run out moves and his clump of five stones is captured.

Dia. 5. No escape 2
Dia. 5. No escape 2
After Black 7 in Dia.3, White's strongest resistance is to play a hane at 8. In that case, Black connects with 9. White has to connect at 10, but, after Black 11, it is clear that White loses the capturing race.

In conclusion, intuition is not something mysterious that comes into our consciousness from out of the blue or from some unknown realm that inspires us. It comes from a broad knowledge of general principles, shape, and, in particular, tesujis.

Recommended reading
For the novice player who aspires to reach dan-level strength, the best book for studying tesujis is A Survey of the Basic Tesujis. It presents 38 tesujis, each one introduced with a simple example, followed by a number of straightforward, uncomplicated, kyu-level problems. If you are a kyu-level player, I believe that diligent study of this book will increase your playing strength by two stones.