Scatter dots on a page so no three ever line up perfectly. Is that actually possible?
Take any finite set of points on a page, as long as they don't all sit on one single straight line. A mathematician asked: must there always exist at least one line that passes through exactly two of the points, and no others? Or can you always find some clever arrangement that avoids this?
Reveal the answer
Such a line always exists, no matter how the points are arranged, as long as they aren't all collinear to begin with. James Joseph Sylvester posed the problem in 1893, but it went unsolved for decades until Tibor Gallai finally proved it in 1944, and it's now known as the Sylvester–Gallai theorem, a foundational result in combinatorial geometry.