Tentaizu...

Tentaizu is a game I saw in an airline magazine. I liked it very much because it's solution requires both algebra, reasoning and partitioning, all depends on the complexity. I developed it for Android platform. It can be played with any size of board but due to screen limitation we provided either 4x4, 5x5, 6x6 of 7x7 boards.

The player has to locate a given number of stars within a number of hidden cells on a board. Tentaizu is similar to mine-sweeper in terms of general game rules. However, it does not include any randomness. There is a unique solution all the time.

The binary variables can be used to establish a mathematical equality or

inequality with reasoning to get a solution locally. Sometimes you need

to partition the board into small isolated zones and find solution to

each zones.

Some examples of the equations are as follows:

Let a, b and c are unsatisfied invisible cells that around a visible

cell with value of 3. The variables a, b and c can take only "1" or "0".

"1" means that a star is hidden, "0" means that no star is hidden.

Then, we can write

a+b+c = 3

Since a, b and c are binary variable, then only one solution exist:

a=1, b=1, c=1.

Another possible form of equations is as follow:

a+b+c+d+e=4
a+b+c=2

Then subtracting the second equation from the first one:

d+e = 2

This means that d=1 and e=1.

One more possible case is as follow:

a+b+c+d+e+f = 1
a+b+c=1

This implies that d+e+f = 0, and therefore d=0, e=0, f=0.

The last example is as follow:

a+b+c+d = 3
c+d <= 1

Then, a+b = 2 and c+d = 1. Here a=1 and b=1.

It helps you to give a short quality break in your daily activity. The solution can be reached in a few minutes in most cases.