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There is an square. Write a into 24 squares and one into 1 square, such that by using the step below as many times as you need, you can achieve that every square contains a .
Choose a or a square, and change each sign in the square (form to , and from to ).
How many places could be the in the beginning?
Note: Each square must contain exactly 1 sign.
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1 solution
Each square larger than a 1 × 1 square will contain an even number of blue squares. So if the - sign in the beginning is in a blue square, then after a step there will be an odd number of - signs in the blue area (it doesn't matter which type of square do we chose). Therefore the - sign will be on a yellow square.
Each square larger than a 1 × 1 square will contain an even number of red squares. So if the - sign in the beginning is in a red square, then after a step there will be an odd number of - signs in the red area (it doesn't matter which type of square do we chose). Therefore the - sign will be on a green square.
There is only one square, which is in both of the yellow and the green areas: the middle 1 × 1 square. Here is an example:
