I built an interior cat flap for $11.

[Xist]

The cat constantly wants to go back and forth.

Mom uses a slipper to keep her door ajar and I started using a shoe, but just a couple inches of air gap lets in a distracting amount of noise, so I had different ideas, but we already had some $10 pairs blackout curtains, so I bought cord from Dollar Tree, clipped an end to a pen, fed it through, and hung it on the other side of the door.

I just need to figure out how to get it to automatically close.