Nice illustration. It also lends itself to drawing an analogy between a solution to the Noddy Problem and real life akrasia. In the Noddy problem, the obvious solution is to make sure that the duplicate is not identical (or rather, that their environment is not close enough to yours in the relevant ways). One way to do this is by changing incentives -- you know that you would pick up Noddy if your life depended on it, so you can create a duplicate that believes that it will explode if they don't do the job. In the real world, you can apply the same sort of solution by using self-binding to coerce your future selves into doing your bidding.
An episode of the Noddy animated series has the following plot.
Noddy needs to go pick up Martha Monkey at the station. But it's such a nice, sunny day that he would prefer to play around outside. He gets an idea to solve this dilemma. He casts a duplication spell on himself and his car and tells the duplicate to go fetch Martha while he goes out to play. Later, Noddy is out having fun when he suddenly spots his duplicate. It turns out that the duplicate also preferred playing outside to doing the errand so he also cast a duplication spell. Then they see another duplicate, and another...
I think this story makes for a nice simple illustration of one of our perennial decision theoretic issues: When making decisions you should take into account that agents identical to yourself will make the same decision in the same situation. A common real-life example of the Noddy problem is when we try to pawn off our dietary problems to our future selves.