The Maths Thread

One minute to think of this solution. I must be a genius.

Note - not to scale.
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View attachment 115691
Is that allowed? (oh read the question wrong, flip the shading/unshading)
That's what I initially thought of. But then I thought... how would I actually go about accurately shading the perimeter of the inner square? Which led me to think about, perhaps folding the larger square in half or perhaps along the diagonals to assist in shading... Hmm... Which then led me to think about each of the 4 sub-squares. How do I go about shading exactly the right amount of each of them... hang on, the right amount is 1/2! And bingo!
 
That's what I initially thought of. But then I thought... how would I actually go about accurately shading the perimeter of the inner square? Which led me to think about, perhaps folding the larger square in half or perhaps along the diagonals to assist in shading... Hmm... Which then led me to think about each of the 4 sub-squares. How do I go about shading exactly the right amount of each of them... hang on, the right amount is 1/2! And bingo!
Genius.
 
For anyone with a liking of logic puzzles, have a look at these.


The basic premise is a given number of stars (1, 2 or 3) are to be placed on each row, column and in each shape, with none touching in any direction including diagonally.

My son tells me all puzzles should be solvable using logic alone. I have my doubts.

For anyone familiar with the game, can you spot anywhere I could add an x below. The last one I could find is the white square one. This game is supposed to be of normal difficulty level.

Link to this game here: https://www.puzzle-star-battle.com/?e=NzoxNyw4MzksNTQ0

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