On a grid of dots, connect 4 dots to make a square. Easy when the sides are horizontal — but tilted squares count too.
Tilted squares count too
On a grid of dots, a square doesn't have to sit upright. Corners at (0,0), (1,2), (3,1), (2,−1) make a perfectly real square: every side is √5 long and every angle is 90° — it's just rotated. Spotting these is secretly a Pythagoras hunt, because each side length comes from a right triangle on the grid.
On a 3×3 dot grid you can find 6 squares (4 tiny, 1 medium, 1 tilted). On a 4×4 grid there are 20. Try to list them all before peeking.
A grid square has corners (0,0) and (1,2) as one side. How long is that side, and what's the square's area?
Tilted squares are real
A square with corners at (0,0), (1,2), (3,1), (2,−1) has all sides equal (√5) and all angles 90°. It's a square, just rotated.
On a 3×3 grid you can find 6 squares: 4 small, 1 medium, 1 tilted. On a 4×4 you can find 20. Counting them is a Pythagoras puzzle in disguise.