Problem is whether each square of the given board be labeled with pictures of Cats(0) and Dogs(1) so that every neighborhood is odd. A neighborhood of a square is the set of squares sharing an edge (sides) with this square and does include itself.

A neighborhood is odd if there are an odd number of squares with pictures(labels) of Dogs(1) in the given board.

Following picture shows a 4 x 4 board configuration with the desired labeling :

1 1 0 1
1 1 1 0
0 1 1 1
1 0 1 1

Iniatially all the small squares are labelled with the pictures of Cats(0).

The 4 corner squares have 3 neighbors including itself. Any other square on the 4 boundaries (except extreme corners) have 4 neighbors including itself. Any other square has 5 neighbors including itself.

Red circled Dog or Cat means that Square has even neighborhood.

Green circled Dog or Cat means that Square has odd neighborhood.

*** Your target is to achieve odd neighborhood for all the squares and try to do it in minimum number of moves.

In complex mode your target will be to make all the squares green circled.

In simple mode all the squares are labelled with 0 or 1.

In complex mode all the squares are labelled with Cat or Dog. Cat corresponds to 0 and Dog corresponds to 1.

If a square is clicked its status are toggled i.e 0(Cat) changes to 1(Dog) or 1(Dog) changes to 0(Cat).

You can switch between simple and complex mode keeping the same board size.

Clear button clears the board.

This game is highly challenging to improve your analytical and visualizing skill.

This game is a simple demonstration of advanced mathematical theory.

This app is completely free and contains no ADS or IN-APP purchase.

In case of any bug please let me know through email.