Sudoku

Sudoku is a game that consists of 81 cells made up by a 9x9 grid of cells this then has 9 regions of 3x3 grids each containing 9 squares. Each number 1 through 9 exists exactly once in each row, column, and 3x3 region. Your job is to give each of these cells a number with no interference, solving the grid.

Clicking on a open tile will increment this space by 1, starting at blank going to 9 and repeating the cycle when clicked again.

Disclaimer: The term "group" here will refer to any 3x3 region, row, or column.

Rules

Direct rules of the sudoku game

1. All cells have to have a possible number
2. A number cannot exist twice in the same 3x3 region, row, or column
3. A number cannot be omitted from any 3x3 region, row, or column

LEGUP Proof Rules

Case Rules

Possible Numbers for Cells

If a tile can be any certain numbers based on the state of the board, branch off for each of those numbers.

Possible Cells for Number (Region/Row/Column)

If a number can be in only certain cells of a group, branch off for each of the cells.

Contradiction Rules

Repeated Number

This is a direct violation of rule #2. If a number exists twice in a group the board is in a state of contradiction.

No cell for number

This is a direct violation of rule #1. If a number does not exist in a group and cannot exist in any of the current open cells the board is in a state of contradiction.

No number for cell

This is a direct violation of rule #3. If a cell cannot contain any number the board is in a state of contradiction.

Basic Rules

Last number for cell

This rule is extended from rule #1. If only one number is left to be possible for this cell, this cell must contain that number.

Last cell for number

This rule is extended from rule #3. If only one cell in a group can contain a number, that cell must contain that number.