Why does this "Cannot create property text on String" error happen?

i have 3 text boxes(textbox1, textbox2, textbox3) on stage want single message passed onto each text box can't seem work. code below keeps getting error message: "cannot create property text on string." how make "textbox" not string.

var textboxes:array = new array();

var winnertext:string = "you won";

var randomnum:number = math.ceil(math.random() * 3);
var i:int;
var n:int;
for (i = 1; <= 3; i++)
{
textboxes.push("textbox" + i);
n = i-1;
textboxes[n].text = winnertext;
}

you need textfield instance. example:

textboxes.push(new textfield());
textboxes[n].text = winnertext;

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