The core game has 9 rules (less than Chess).

-For most players, the game is learn by pressing buttons in an initial game. (Takes about 10 minutes first time.) This would take the form of a tutorial for single player vs. computer.

-The instructions in-app will be a pictorial slideshow, not text.

Here is the concise rule description. (Warning: non-Engineers tend to find it incomphrensible, thus the above emphasis on tutorial and pictorial description. But for Engineers, these two short paragraphs are incredibly impressive:)

M Rules (Concise)
The game is played on an n²*n² gamegrid divided into n*n subgrids, using n² integers, typically 0 through z²-1. Players take turns placing integers into boxes, and receive equivalent points in the native region, where native region is the region in which the integer is placed. They also receive 1/2 points in all adjacent regions touching the integer’s box, both orthogonally and diagonally. Placement must conform to the rules of sudoku, where an integer may only be placed once in a given column, row or region. When all integers that can be placed have been placed, or by mutual consent of all players, the gameboard is resolved.
Resolution begins in the region(s) with the greatest point disparity (Δ) between contesting players. A region is awarded to the player with most the points in that region, known as the dominant player. When a region is awarded, the dominant player is said to have control, and all opposing integers in the region flip, converting to the controlling player. All points derived from the flipped integers are re-assigned to the controlling player, including points applied in adjacent regions. When all regions have been resolved, the player who controls the most regions wins.
[Note: n refers to non-negative integers only, z refers to positive & negative, typically used for integers that are played.]

Another way to explain it is:

-You play on a Sudoku board. Numbers represent structures (8=Walled Town, 7=Castle, 6=Fort, ect.)

-When you place a structure in a region, it exerts power in that region with a point value equal to it’s number. If the structure touches any neighboring regions, it exerts influence over those regions with a point value equal to half it’s number. These points are armies.

-When all structures have been placed, war breaks out.

-Regions are contested if more than on player has structures or influence in that region. The battles over contested regions go in order of the highest imbalance between opposing forces.

-When the battle for a region is over, it is awarded to the player with the most points in that region, and all the structures go over to that player, with all of the corresponding points.

-When the battles over all contested regions is complete, the player controlling the most regions wins.