Question 4
In the following $6\times6$ array, one can choose any $k\times k$ subarray, with $1<k\le6$, and add $1$ to all its entries. Is it possible to perform the operation a finite number of times so that all the entries in the array are multiples of $3$?
$$\begin{bmatrix}2&0&1&0&2&0\\0&2&0&1&2&0\\1&0&2&0&2&0\\0&1&0&2&2&0\\1&1&1&1&2&0\\0&0&0&0&0&0\end{bmatrix}$$
Original source array:
$$\begin{bmatrix}2&0&1&0&2&0\\0&2&0&1&2&0\\1&0&2&0&2&0\\0&1&0&2&2&0\\1&1&1&1&2&0\\0&0&0&0&0&0\end{bmatrix}$$
Original source array: