How can I visually explain M of N encryption (Shamir Key Sharing)? I'm trying to find a simple way to explain M of N keys to end users, where 2 keys would unlock something. 

So far, all I found was this complex example where the key threshold was 1 (just one key of any lock will unlock this):



Larger version here.

Lacking any commonly accepted illustration, or image, is there any visual way to express M of N keys (Shamir Secret Sharing)?
I've used the following a number of times in lectures, and it always goes over well with a technical audience.


I start by asking them How many points do we need to uniquely define a line? The answer I get back is always 2.
Next I ask If I give you a single point in the X,Y plane, how many lines can you draw through that point? The answer I always get back is infinite.
Finally I say, Let's consider I have some secret (usually I use 42 for the obvious reason) and I want to share this secret with many people so that any two of them could get together and reconstruct the secret.


At this point, depending on the audience, I will either ask how I could accomplish this, hoping they get the idea to somehow encode 42 into the line (e.g., as the y intercept). Or, I will just tell them how it works.

All of this can be shown visually, which I would try to add pictures here, but I don't have time at the moment.

For even non-mathematical audiences, if I start with #2 above (draw a point on the board or in a slide and ask how many straight lines can be drawn that pass through this point), it works well. Then I move to #1, then #3.