How to model a letter K (or any other object made out of transformed copies of itself)?

Question

I've elongated a cube and copied it twice. I've then manipulated those two copies to look like the two non-vertical parts of the K, partially intersecting the vertical part. I then tried using booleans to merge the geometries into a single object.

However, when I try unioning two objects, one disappears. I've looked and it seems to be because of the duplicated geometry (the fact that I copy and pasted it?), but I can't really help it here, and remove duplicates removes 0 vertices.

How do I properly merge three objects that are transformed copies of one another?

Answer 1

1. Add a cube and Z upscale it;
2. Copy it with Shift+D;
3. Move the copy +1 grid step along X axis and shear it;
4. Combine the two cubes;
5. Use mirror modifier.