3x3x1 Twisty Puzzle aka Floppy Cube

Vocabulary: R means twist the Right side 180 degrees. T means twist the Top. L means twist the Left. B means twist the Bottom. Adjacent means next to.

Recently Alex got a new 3x3x1 Fidget Spinner. It looks great. It turns great. But the centers are both black, so it makes for a slightly different solving experience. If you solve the edges first, then sometimes after you solve the corners, all the edges are flipped. One way to deal with it is to do LTRB TRTR. Or the equivalent. But I want to know if there is a way you can study the scrambled puzzle and know whether the front needs to be yellow or white before you start solving it. 

I think I have it figured out but I am having trouble putting it into words. Let me try. One thing I will say is that all my scrambles are done with 180 degree turns, so that the puzzle is a 3x3 square after each turn. No weird shapes at this stage. OK. Let's go.

Scramble it.
Are any corners in the correct place? If so, but if the color on front does not match the color of the two adjacent edges, that means those edges need to flip. Think through the different ways to flip the edges that need to flip, keeping in mind where the corners end up. If you can do it in such a way that all 4 edges are solved and only one corner is solved you can use the 4 move 3-cycle to complete the solve. Some examples of the 3-cycle: RTRT takes the bottom right corner to the top right corner to the top left corner. LTLT takes the bottom left to the top left to the top right. BRBR takes bottom left to bottom right to top right.

Sometimes after a scramble a corner is in the right place but only one adjacent edge matches. That means the other one needs to flip. Try to think through the moves needed to solve it, then do it.

Sometimes after a scramble none of the corners are in the right place. On a solved puzzle do RLT RLT. This is one example. How would you describe it? The top two corners need to swap and the bottom two corners need to swap. And the corners don't match the edges. What if both pairs of diagonal corners need to swap? RTL RTL. RTR LTL also works, and I think it is easier to execute. With this double swap, the corner front color matches the edges. These algorithms are great if all 4 edges are the right color, but what if 2 are white and 2 are yellow? Try this on a solved puzzle. RLT RLT RTRTRT. It's a TB double swap, but 2 edges are yellow and 2 are white. If you go LB, all the edges are the same color and only the Left Bottom corner is in the right place. It's color matches the adjacent edges and RTRT is the 3-cycle needed to solve the other corners. But! What if instead of LB to make the edges match, you had gone RT? Then the solved corner does not match the adjacent edges, so you know LB was the right way to go, and not RT.