Quiz

I saw it on another forum, but I don't remember exactly how it was described there. At first, I, like Ment, thought that the spider should intercept it perpendicularly, but then one guy proved that for an equilateral triangle, if it intercepts it at a 60-degree angle, it will be faster. I then built a dependency of the ratio of the distance traveled by the spider to the distance traveled by the ant on the angle, found its derivative, and realized that yes, it will be minimal when the spider runs at an angle of 60 degrees to intercept the ant, and not at a right angle (and for the triangle, the speed will be greater than v/2). And for a regular tetrahedron, since its edges are inclined at an angle of arccos(1/3^1/2), the path that the spider must travel must be multiplied not by cos 60, as in the triangle, but by cos(arccos(1/3^1/2)), that is, the spider's speed should be as Ment said.