A $2\times2$ ColorSaw

The pieces of this ColorSaw have been flipped, rotated and moved.

Can you reassemble the puzzle so that each adjacent side has the same color/shape?

• what is a colorsaw? thanks! Jun 5 '19 at 6:22
• It's like a JigSaw, but with colors not jigs.@OmegaKrypton
– JMP
Jun 5 '19 at 6:47
• Is Tetravex the original name btw? Jun 5 '19 at 11:00

Looks possible to me.
1. Rotate the top left square by 90 degrees clockwise
2. Rotate the bottom left square by 90 degrees counterclockwise.
You'll get this picture:

3. Keep the top left square where it is and shuffle the other three around:

I'm afraid not much logic was involved - I started trying to show that it's impossible and came up with a counterexample :-)

Second solution with each symbol matched.
I wasn't happy with my first solution because the red stars are not oriented the same.
This is simpler and more pleasing:

- slide top right down
- slide bottom right across
- slide bottom left up
- slide top left across and rotate 90° clockwise

- if one must be flipped, let's flip the one with 2 red stars because it is symmetrical

My solution

matches one of each pair

- bottom left stays put
- top left slides to bottom right
- bottom right slides up and rotates 90° anti-clockwise
- top right slides left, flips vertically and rotates 90° clockwise