by applying linear algebra. The following is an example for applying the subtraction of two equations: a + b + c + d = 3 c + d = 1 The first statement has four variables whereas the second statement has only two variables. The latter one means that the sum of c and d is 1. Using this fact on the first statement, the equations above can be reduced to a + b = 2 c + d = 1 The algebra on a board A game based on the algebra with binary variables can be visualized in many different ways. One generic way is to represent the right side of an equation as a clue in a cell (clue cell), and the neighbors of a clue cell as variables. A simple case is shown in Figure 1. The neighbors can be assumed to be the up/down, left/right, and corner cells that are sharing an edge or a corner. The white cells may contain a hidden object or nothing. In other words, they are the binary variables. They take place on the left side of the equations. Each clue cell, a cell with blue background in Figure 1, contains a positive number corresponding to the number of its neighbors that have hidden objects. The total number of the objects on the board can be given as an additional clue. The same board with variables marked is shown in Figure 2. The reduction into a set of equations with binary variables The main equation is written by using the total number of the hidden objects given. From the first figure this corresponds to the following equation a + b + c + d + e + f + g + h + i + j + k + m = 3 The other equations are composed one by one for each clue cells: a + b + c + e + f + h + i + j = 1 f + g + j + m = 1 h + i + j + k = 2 i + j + m = 2 Although there are several ways to solve the equations above, the following explicit way can be applied: It is known from the equation set that i + j + m = 2. However, since j and m are neighbors of a cell with number 1,