The most starting points were the two perfect squares: the Light Blue 9 (which must be a 3x3 square) and the Grey 4 (which is almost certainly a 2x2 square). In an 8x8 grid, a 3x3 square has limited placement options. By testing its fit, you quickly find its home in the upper-right quadrant.

The next key piece is the Red 7. As a prime number, its shape is fixed to a 1x7 or 7x1 strip. Seeing the 3x3 square in place, it becomes obvious that the Red 7 fits as a 1x7 vertical strip running alongside it. This is the first major chain reaction.

The puzzle included two fixed 1x1 blocks. These are non-negotiable anchors. The fixed green block on the right side must be part of a larger piece. The most likely candidate is the Grey 4. Placing the 2x2 Grey 4 to cover this anchor locks in the bottom-right corner.

With the Blue 9, Red 7, and Grey 4 all placed, the entire right side of the grid becomes highly constrained. The remaining gaps create perfect, unmissable slots for the smaller pieces like the Green 2 and the Blue 2, which fall into place neatly.

Attention now shifts to the left edge. The fixed orange block must belong to the Orange 5 piece. The only logical fit is a long vertical strip. Similarly, the Green 3 at the top-left corner naturally forms a 1x3 strip. Placing pieces along the outer boundary is a strategy because it simplifies the complex interior space.

With the borders defined, the central column is all that remains. The Teal 6 (as a 3x2) is the largest remaining piece and has a clear spot. The rest of the pieces (Purple 3, Pink 2, etc.) now have only one possible orientation to fill the remaining gaps, completing the puzzle.