Puzzle 1 and Puzzle 2
Puzzle 1 features a series of shapes attached to a rectangle by long lines. Click on one of the shapes and it moves from the outer border to the inner one (or vice versa). After playing around with it for a few seconds you'll realize that each click shifts every line of the same color or shape as the one you clicked on. For example, if you click on a green heart, every green shape and every heart shape (regardless of color) will slide to a new position. The goal is to slide all shapes into their correct position such that all shapes turns color (they will be grey if in the wrong position), and it's certainly not as easy as it sounds. This first game is a great example of a puzzle that doesn't make sense at first but can be deciphered with a little bit of experimentation.
Tonypa's second entry is a bit more abstract. You face an 8x8 grid of colored tiles and can scroll through a larger 8x8 grid with the arrows. A row of numbers sits at the bottom waiting for you to type. As you surf through the grids your brain is frantically trying to make sense of it all. The fun of Puzzle 2 is in figuring out how the game works, so I'll save any spoilers and let you work it out on your own. Just take note of the number of squares and the colors and you're on the right track.
Tonypa has a bit of a reputation for captivating flash games, and these two competition entries really show off his talent and creativity. They both fit the theme very well and are engaging games in their own right. Puzzle 1, Puzzle 2