Anett is drawing X-es on a 5×5 grid. For each newly drawn X she gets points in the following way: She checks how many X-es there are in the same row (including the new one) that can be reached from the newly drawn X with horizontal steps, moving only on fields that were previously marked with X-es. For the vertical X-es, she gets points the same way. a) What is the maximum number of points that she can get with drawing 25 X-es? b) What is the minimum number of points that she can get with drawing 25 X-es? For example, if Anett put the X on the field that is marked with the circle, she would get 3 points for the horizontal fields and 1 point for the vertical ones. Thus, she would get 4 points in total.
Problem
Source: (2021-) 2022 XV 15th Dürer Math Competition Finals Day 1 E2
Tags: combinatorics