Go Wizardry

Correct Solution 1 (Consecutive Moves with Purpose)

Capturing the stones in the corner is the coup de grace. The diagonal attachment of White 1 followed by 3 occupy the vital points in this shape.

Correct Solution 2 (Five Point Oversized Eye)

The connection of Black 4 brings on White 5, leaving Black with a single five point oversized eye. If Black 4 at 5, the White capture at 4 precludes the possibility of ko.

Diagram 1 (Failure)

Pushing in at White 1 allows Black to play at the vital point with 2, resulting in the necessity to fight a ko. Should White use 1 to capture at "a," Black 4 still produces ko.