Let n≥4 be an even integer. Consider an n×n grid. Two cells (1×1 squares) are neighbors if they share a side, are in opposite ends of a row, or are in opposite ends of a column. In this way, each cell in the grid has exactly four neighbors.
An integer from 1 to 4 is written inside each square according to the following rules:[*]If a cell has a 2 written on it, then at least two of its neighbors contain a 1.
[*]If a cell has a 3 written on it, then at least three of its neighbors contain a 1.
[*]If a cell has a 4 written on it, then all of its neighbors contain a 1.Among all arrangements satisfying these conditions, what is the maximum number that can be obtained by adding all of the numbers on the grid? inequalitiescombinatorics unsolvedcombinatorics