Is it a magic box?
From your description, it doesn’t sound like a Rubik’s cube, a magic tower, or a three-dimensional puzzle piece.
The magic box I'm talking about is a small wooden box that looks ordinary, but it really can't be opened without using your brain.
I once bought one as a gift for a friend.
This kind of thing is sold in places that specialize in educational toys, and it is also sold in some gift shops. It should be pretty easy to find. I guess there is one in Xidan.
In addition, there are many educational toys, such as Kong Ming Lock, Kong Ming Qi (Single Noble), Nine Links, Tower of Hanoi, etc., all of which are relatively classic styles. On this basis, many varieties have been developed.
Go to a specialty store and check it out, there are many styles.
However, when giving gifts, it is still recommended to use simpler styles, not too complicated. It will not be good if your friends don’t know how to play with them when they get them.