I recently wrote an essay, Thinking Inside and Outside the Box, which starts with a famous nine-dots puzzle that kicked off the expression: thinking outside the box. Here is another puzzle with the same nine-dots setup.
Puzzle. What is the smallest number of squares needed to ensure that each dot is in its own region?
Usually, people who try to solve this puzzle come up with the following four-squares solution.
As with the classic nine-dots puzzle, they imagine that the dots are on a grid and try to build squares with sides parallel to the grid lines. What would be the outside-the-box idea? The sides of the squares would not need to be parallel to the grid. This way, we can solve the puzzle with three squares.
One of my MathRoots students offered a different and awesome solution also using three squares.