In the image, we can see a square formed by circles that has been colored with four colors (red, yellow, green or blue). In it we can verify that there are monochromatic rectangles or squares, that is, that there are four points of the same color that form the four corners of a rectangle or square.
Are you able to modify the colors of one or more of the points that form the square in such a way that there are no rectangles or monochromatic squares, that is, that there are no four points of the same color that form the four corners of a rectangle?
Extracted from the page mathlesstraveled.com
Changing a single point, we get this square without rectangles or monochromatic squares inside:
You can find more information on the mathlesstraveled.com page.