Pretentious Title: SquareLogic is an abstract puzzle game that takes the concept behind sudoku and twists it to create something far more interesting and engaging. Like sudoku, the goal is to fill a square grid such that the numbers appear only once in each column and row.
SquareLogic's twist on the formula is in the cage system. Instead of prepopulating the grid with enough numbers to solve the puzzle, SquareLogic divides the board into arbitrary chunks, called cages, and assigns a mathematical rule to each. For instance, one cage may require its content to sum to 8, another may require its smaller value to divide the larger value 4 times. Other cages impose inequality operators on the divisions between cages, indicating that one square must contain a larger or smaller number than its neighbor. The puzzles have extra mechanics beyond the cages as well, including double-puzzles, where two grids contain the same solution but different cages, each providing too little to solve on its own, but enough to solve when paired with the other. Other puzzle types may leave some cages unfinished and require the player to paint them in as they go.
This formula would likely be overwhelming and tedious, especially on full-sized 9x9 puzzles (the game ranges from 4x4 to 9x9). However, the game automatically removes numbers from tiles when that number is used elsewhere in the column/row, and players can right click any number to remove it as a viable option. This effectively automates the more menial part of the puzzle, leaving the logical problem solving front and center. The game also highlights possible valid combinations for cages in a small window, so you don't have to constantly keep a calculator by your side to determine what factorizations are possible for a number set. Because of these features, the puzzles go by quickly and rarely feel like they're ever wasting your time.
SquareLogic isn't flawless though. The 4x4 puzzles are almost comically easy due to their small size, while the 9x9 and some 8x8 puzzles can become frustrating and tedious because there is simply too much information to pore over. It becomes less a game of applying logic and more of a mindless search for the next clue you can use. Luckily, the game still has plenty of 6x6 and 7x7 puzzles, which feel extremely well paced.
Another problem is the immediate error highlighting feature. When you first boot up the game, go into options and turn this setting off immediately. This setting causes the game to tell you the very instant you make a mistake. It's a feature that is quite literally too helpful, as it quietly encourages you to start guessing whenever you begin having trouble. With this disabled though, there's still an incredibly nice hint feature to help you out of jams. Rather than openly tell you what's wrong, it simply highlights a section of the grid where you should be able to either eliminate possibilites or find a correct number. It's especially useful on the large puzzles where it's easy to have too many options to pore over.
The one last problem is somewhat debatable. The game simply has too many puzzles. It has 6 regions, each with a staggeringly large number of available puzzles. The first area alone contains 4800. That is not an exaggeration. While it certainly means the game has incredible value, it can be a little disheartening to know that you're not likely to ever even come close to finishing all of the puzzles. Oh, and anyone obsessed with achievements would do well to avoid this game for that reason, unless you want to solve all 4800 puzzles in the first region for a cheevo.
Overall, for anyone who likes abstract logic puzzles, SquareLogic is pretty much top class. It's fun, mostly well paced, has a ton of puzzles and lots of good mechanics. Well worth the $5 asking price.