Ask HN: When will AI be able to write efficient code to solve this puzzle?

You are given an array of n x n integers. The goal is to end up with an array in which all entries are equal. Four kinds of moves are allowed: (1) rotate a row (2) rotate a column (3) add 1 to all entries in a row (4) add 1 to all entries in a column A "rotation" means you shift the items one position in the row/column (in either direction) with wrap around. First, show the goal is achievable if and only if the sum of the numbers in the initial configuration is congruent to 0 mod n. Then, write an efficient python program to solve the puzzle whenever it is possible to do so.