The most opening move was the Dark Purple 8. Positioned on the bottom row of an 8-wide grid, the probability of it being a clean 8x1 strip was extremely high. Any other configuration (like a 2x4) would create awkward, often unfillable gaps. Locking it in as an 8x1 strip set a firm foundation for the entire lower half of the grid.

With the bottom row solved, the Pink 4 was the next domino to fall. Its clue was positioned in a way that made a 2x2 square the most natural fit. The 8x1 strip below it eliminated any possibility of a 1x4 vertical rectangle, forcing it into the 2x2 shape. This is a classic example of one piece defining the options for another.

Placing the Pink 4 immediately defined the bottom-left corner of the Yellow 10's territory. Given the remaining space along the right-hand wall, a 2x5 vertical rectangle was the only logical configuration for the Yellow 10. This placement, in turn, walled off the space for the Dark Green block, confining it to a 1x6 vertical strip. We solved the entire right third of the puzzle in three moves!

Attention then shifted to the center. The Green 4 was another piece begging to be a 2x2 square. Placing it as such forced the adjacent Light Purple 2 into a 1x2 vertical strip. These two placements then created a perfect 2x4 slot for the Red 8.

The remaining unassigned cells on the left were then filled by deduction. The Orange block in the top-left corner was boxed in by the pieces we'd placed, forcing it into a 2x3 shape (Area 6). This left two final rectangular spaces for the Light Blue 6 and the Dark Blue block's shape (which also ended up being a 3x2 rectangle, Area 6).