Preliminary algorithm/brainstorming.

A main Board class consisting of

• Array of Cells
• List of CellGroups

Array of Cells

• each item in this 2D array would represent each cell of the game
• has a solution value (or blank if one is not found yet)
• has a list of possible solution values

List of CellGroups

• A cell group represents a collection of cells that amount to the group's value based on the action described. ex. 5+ would mean that this Cell-Group individual values should add up to 5
• a list of Cell references. ex. a particular CellGroup is including Cells[1,1] and [1,2]
• this class would most likely include most of the game-solving logic.

Preliminary solution logic. I think I will employ something that resembles a "queue" here (//toexplain). Rough logic steps for first few hundred puzzle boards (that are granted to be very simple) in priority order from highest to lowest...

• Cell's possible-solution contains only one item or Cell text value contains a "=" then set the Cell's solution value
• Cell's possible-solution contains only one item from the Cell-Groups possible solution values then set the Cell's solution value

Hah! pretty simple to start out with, I think.

Keeping in mind the most general rule of this number game - one unique number per row and column no matter the cell-group rules -- the "queue" I mentioned will work something like this

• Anytime a Cell's solution value is set, queue up a possible solution value eliminating method from all cells in the same row and column
• From the bullet above any time a Cell is down to one possible solution value queue up a Cell's solution value to be set... naturally resolving in a recursive loop.