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Damn...
It is obvious now of course but... I thought the CardLayout is a little different than others and so I do not need this:

rightPanel.add(panelOne);
rightPanel.add(panelTwo);
I...

Okay. This is my main class, only calls the GUI:

public class SolveHere {

public static void main(String[] args) {
SolveSomehow m = new SolveSomehow();
m.setVisible(true);

}
}

Norm, I hope this is enough for you to help me. The attached file includes my source file and a compiled app. The source and app only have the codes about the CardLayout.

I have a JFrame, a JSplitPane as the container of the frame.
On the left side of the splitpane, there are two radio buttons (more to come, but I am stuck).
On the right side, there is a...