The most logical starting points were the Gold 3 in the top-left corner and the Green 5 on the far-right edge. Gold 3: A 3-patch can only be 1x3 or 3x1. Placed as a 1x3 horizontal strip, it would completely wall off the Teal 6 clue. Therefore, it had to be a 3x1 vertical strip. This was the first domino to fall.

Similarly, a 5-patch is either 1x5 or 5x1. Since its clue is in the rightmost column, a 1x5 horizontal shape is impossible. It was locked in as a 5x1 vertical strip.

Solving the Gold 3 (3x1) immediately forced the hand of the Teal 6. To fit in the space next to it, the Teal 6 couldn't be a 1x6 or 6x1. It had to be a 3x2 rectangle (3 tall, 2 wide) to align with the Gold 3.

The Green 5 (5x1) defined the entire rightmost column, leaving only one cell open at the top. This forced the Red 2 and Purple 2 patches to be 1x2 horizontal strips, as there was no room for them to be 2x1 vertical shapes.

The next major move was the Dark Blue 6. Its clue is in the bottom row. While it could theoretically be a 2x3 or 3x2, the most and likely solution is a 1x6 horizontal strip that fills the entire bottom row. Placing this created a solid "floor" for the puzzle.

With the bottom row filled by the Dark Blue 6, the Orange 6 was squeezed. The available space was 2 rows high and 3 columns wide, locking it in as a 2x3 rectangle.