MathDB

Let

n

be a positive integer. In an

n\times n

garden, a fountain is to be built with

1\times 1

platforms covering the entire garden. Ana places all the platforms at a different height. Afterwards, Beto places water sources in some of the platforms. The water in each platform can flow to other platforms sharing a side only if they have a lower height. Beto wins if he fills all platforms with water. Find the least number of water sources that Beto needs to win no matter how Ana places the platforms.

4

Problems(1)