Question 48
Suppose that the numbers $\{1, 2, \dots, 25\}$ are written in some order in an $5 \times 5$ array. Find the maximal positive integer $k$, such that the following holds. There is always an $2 \times 2$ subarray whose numbers have a sum not less than $k$.
An $5 \times 5$ array must be completed with all numbers $\{1, 2, \dots, 25\}$, one number in each cell. Find the maximal positive integer $k$, such that for any completion of the array there is a $2 \times 2$ square (subarray), whose numbers have a sum not less than $k$.
An $5 \times 5$ array must be completed with all numbers $\{1, 2, \dots, 25\}$, one number in each cell. Find the maximal positive integer $k$, such that for any completion of the array there is a $2 \times 2$ square (subarray), whose numbers have a sum not less than $k$.