The grid is 7x7. Look immediately at the extreme left and right columns. On the left, we have the Yellow 2 and Dark Pink 5. Because 2+5=72 + 5 = 72+5=7, these two shapes form a complete vertical column (Column 1). Similarly, on the far right, the Red 3 and Grey 4 sum to 7 (3+4=73 + 4 = 73+4=7). This instantly locks Columns 1 and 7 into rigid vertical strips, boxing in the rest of the puzzle.

Prime numbers in Patches (like 5 and 7) are massive strategic gifts because they can only be formed as 1xN straight lines. Look at the Orange 7. Being a 7-area shape in a 7-tall grid, it must be a 1x7 vertical strip. Since Column 1 is full, the Orange 7 snaps cleanly into Column 2 from top to bottom.

The Teal 5 is also prime and must be a 1x5 strip. It cannot be horizontal because Column 7 is blocked by the Red 3. Therefore, it is forced to be a vertical pillar in Column 6, dropping down from the top edge.

With Columns 1, 2, 6, and 7 mathematically walled off, the center collapses. The unmarked Blue patch is trapped in a 1-wide trench in Column 3, forcing it to become a 1x7 vertical line.

The Teal 5 in Column 6 leaves a 1x2 empty gap at the bottom right. The Pink 6 (seeded in row 6, col 4) is forced to stretch horizontally into a 3x2 block to fill this void, which in turn frames the remaining center shapes—allowing the Purple 4 to form a 2x2 square and the unmarked Green patch to form a 2x3 rectangle.