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. combinatoricsgame strategyminimumcombinatorial geometry