Jquery If element has class which begins with x, then don't addClass

I think the matter is in the if condition :

if(!$(this).hasClass('[class^="answerbox"]')) {

Try this :

if(!$(this).is('[class*="answerbox"]')) {
    //Finds element with no answerbox class
} else {
    //The element has already an answerbox class
}

You should take a look at toggleClass and is jquery docs.

See this live fiddle example.

Little tip : instead of n = (n + 1) you can do n++ :).

Edit :

After reading again the question, I did a full working script :

Assuming the Html is :

<div id="box">
    <p>Answer1</p>
    <p>Answer2</p>
    <p>Answer3</p>
</div>

<div id="answerbox">

</div>

jQuery :

var n = 0;

$('#box p').on('click',function(e) {
    e.preventDefault();
    if(!$(this).is('[class*="answerbox"]')) {
        n++;
        $(this).addClass('in_answerbox' + n );
        $(this).clone().appendTo('#answerbox').addClass('answerbox_letter' + n); 
    }
});

See this example here.

You should consider using data-attributes, they'll be more reliable then classes for what you're trying to do.

---

Note that if you want the selector to match only if the class attribute begins with a word, you'll want [class^="word"]. * however searches through the whole class attribute. Be careful though, [class^="word"] will not match <div class="test word"> see here.

Use .is() instead of .hasClass(). The former can be used with CSS selectors whereas the latter can only use class name as a "fixed" string.

if(!$(this).is('[class^="answerbox"]'))

NOTE: This will only work consistently if the element has exactly one class

If you need something that works for multiple class names, check this

var theClasses = $(this).attr('class').split(" ");
var i=0;
var found = false;
while(i<theClasses.length && !found) {
   if(theClasses[i].indexOf('answerbox') == 0) {   // starts with answerbox
      found = true;
   }
   i++;
}
if(!found) {
   // the current element does not have a class starting with answerbox
}