SquarO

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SquarO is a logic puzzle possibly inspired by Minesweeper. It was invented by Marc Lebel, a devoted sudoku fan from France. Played on a square grid, it is a binary determination puzzle, in which circles at the intersections of the grid must be filled using the numbers given inside the squares.
Rules
In standard SquarO, every circle has two possible states: unfilled and filled. The number in each square denotes how many of the square's four surrounding circles are filled.
In the Evil variant, there are three circle states: unfilled, half-filled and filled. The number in each square is the number of filled half-circles in the surrounding four circles. For example, if a square's number is 3, the four circles at its vertices could comprise either:
* one filled circle, one half-filled circle and two unfilled circles
* three half-filled circles and one unfilled circle.
Strategy
In the process of solving a SquarO, a square can be called completed if the correct number of surrounding circles has been filled.
Basic strategies of standard SquarO include:
* Any 4s can immediately be completed trivially.
* If two diagonally adjacent squares are both completed, the other two squares with the same common circle can be trivially completed.
* If a 3 is orthogonally adjacent to a 1, the 3 must have both circles filled on the side opposite the side the 3 and 1 have in common. Similarly, both the circles on the side of the 1 opposite the common side must be unfilled.
* Two orthogonally adjacent squares containing the same number must have the same number of filled circles along their respective sides opposite the common side. As a consequence of this, the previous strategy can be extended to a row or column containing a 1 and a 3 separated by an even number of 2s.
* If a row or column contains two 3s separated by an odd number of 2s, the circles on the outside edges of the 3s must be filled. Similarly, two 1s separated by an odd number of 2s force the circles on the outside edges of the 1s to be unfilled.
Web implementation
The official SquarO website contains a Flash-based implementation. Three grid sizes are provided: 3×3 (16 circles), 5×5 (36 circles) and 7×7 (64 circles). Standard SquarO can be played at Easy, Medium and Hard levels; only at the Easy level do 0s and 4s appear. The Evil variant is also offered, but only for the 5×5 grid size and at a single difficulty level.
The implementation displays the numbers in red or black, depending on whether or not each square has been completed. Recently added is the ability to mark squares that are known to be unfilled.
Tournament
Also on the official website is a tournament gameplay option. In this mode, the player is given 5×5 puzzles in the easy difficulty. The player is timed while attempting to complete three such puzzles, one after the other, as quickly as possible.
In this mode, the colour-changing numbers and marking of squares as unfilled are disabled, increasing the level of the challenge. The player must determine for him/herself when each puzzle is solved and then move onto the next puzzle. If the puzzle is not correctly solved when the player presses Next Grid, he/she instantly fails the whole challenge.

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See Also

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