MathDB

Daniel chooses a positive integer

n

and tells Ana. With this information, Ana chooses a positive integer

k

and tells Daniel. Daniel draws

n

circles on a piece of paper and chooses

k

different points on the condition that each of them belongs to one of the circles he drew. Then he deletes the circles, and only the

k

points marked are visible. From these points, Ana must reconstruct at least one of the circumferences that Daniel drew. Determine which is the lowest value of

k

that allows Ana to achieve her goal regardless of how Daniel chose the

n

circumferences and the

k

points.

Problem Statement