"外で遊びに行く" vs "外へ遊びに行く"


I saw the following 2 options in an exam question:

> 私は__に行く
>
> a. 外で遊び  
>  b. 外へ遊び

The answer is '外へ遊びに行く'

Does 'で' also work here? What's the difference here?




> **外へ** 遊びに **行く** (head outside to play)

-> The implication here is that the actor is not currently outside, and will _head out_ to play.

> **外で** 遊びに **行く**

-> This sounds odd because it means that the actor "goes to play" when he's already outside. It's not really clear where he would be going, if anywhere. 

This is similar to saying something like, " _go out outside_ " in English.

