Funny Past Paper Question

The author of my Cryptography exam has a habit of weaving elaborate stories into the questions to liven things up a little. Here's an example:

You are the holder of a two-part key in a 2-out-of-n secret sharing scheme. Strangely, you have two friends, who find themselves in a similarly privileged position. Unfortunately, one of your friends has the mental capacities of a concussed duckling, and has not actually lost their key, but lost track of which of the two parts is which. If an attempt is made to log on in the morning using the key parts in the wrong order, the usual unfeasibly large stone ball rolls out of the wall and squashes everyone. Equally, if they own up to their supervisor, they will be ejected from their job, and discarded on the scrapheap of humanity. A little harsh, some may say, but that's capitalism for you.

So you decide to try and rectify the situation. By getting together with your other friend (the less careless person) you reckon that if you two pool your key shares, (itself a massive breach of security, but that's what friends are for) you will be able to untangle the problem, and save the day.

Explain your cunning plan.