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I have a Panel with 4 Inputfields and a Button. When a Button is clicked, it shifts itself and adds two Inputfields in its place. Before clicking Button,

enter image description here

and after clicking Button.

enter image description here

I want to know how can I shift Button ?

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You could use Dynamic as in :

iField = Table[InputField[], {i, 2}, {j, 2}];

Panel[Dynamic@Grid[Join[iField, {{Button["Add", 
   AppendTo[iField, {InputField[], InputField[]}]], ""}}]]]
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A recursive solution would allow for the fields to stay intact when adding

DynamicModule[{var = False},
    Column[{Grid[{{InputField[], InputField[]}}],
      Dynamic[If[var, #0[], Button["Add", var = True]]
       ]}]
    ] &[] // Panel

However, you won't be able to go above approximately 50 I think

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