Suppose we mark five points of the surface of a sphere.
Can you prove that however the points are distributed it is always possible to draw a hemisphere that include at least four of the five points in its interior or on its boundary?
This puzzle appears in many places and was included in a maths competition as recently as the early 2000s. but I think it must go back further and may have first been published by Martin Gardner, although I don't have the reference.
Five Points of a Sphere Puzzle
Can you prove that however the points are distributed it is always possible to draw a hemisphere that include at least four of the five points in its interior or on its boundary?
This puzzle appears in many places and was included in a maths competition as recently as the early 2000s. but I think it must go back further and may have first been published by Martin Gardner, although I don't have the reference.