Unless I am demented, which is a distinct possibility, Taipei game #17143 (Expert mode) is impossible to solve. I got it down to the central tower and could go no further. The top tile on the tower is a South. There is another South tile immediately underneath it. Since there are 4 South tiles in all, at least one of the other two cannot be in that tower. But if I use the Peek tool, I see that one is under the Four tile and the other is under the Five tile.
I have posted 4 images of the game to this Dropbox folder:
One shows the start of the game, one shows where I got stuck, and the other two show the Peek results.
I also uploaded the game itself, TP3.EXE, which is a stand-alone program. To try this game, set the Difficulty to Expert, then under Game, select Select Game and fill in "17143".
I always thought that the game generated the configurations randomly by laying down 2 matching tiles at a time. In that case, impossible games would be, well, impossible.