Maximal guaranteed sum of numbers in non-adjacent cells
Source: Caucasus MO 2024, Seniors P4
March 15, 2024
combinatorics
Problem Statement
Yasha writes in the cells of the table all positive integers from 1 to (each number once). Grisha looks at the table and selects several cells, among which there are no two cells sharing a common side, and then sums up the numbers in all selected cells. Find the largest sum Grisha can guarantee to achieve.