Solution of the Week #491 - Grid Fill

These are (I believe) the only distinct solutions for a 7x7 grid.

In general, a solution can always be found that involves one large rectangle or square which contacts all four sides of the grid. Neither of the edges of this rectangle can be a multiple of 3, hence why for the first solution, the main rectangle is 2x5, as 2 and 5 are the only pair of numbers adding to 7 that don’t involve a multiple of 3.