The 8x8 grid has a bottom row exactly 8 cells wide. The clues at the bottom are the Peach 3 and the Dark Blue 5. Since 3 + 5 = 8, these two shapes must share the bottom row as 1x3 and 1x5 horizontal strips.

With the bottom-left corner occupied by the Peach 3, the Orange 7 on the left edge is trapped. It cannot go down to the 8th row, leaving exactly 7 vertical cells above the Peach 3. The Orange 7 is forced into a 1x7 vertical strip.

Look at the right side. The Green 9 and Brown 9 are trapped on the right edge. Since the grid is only 8 cells wide, a 1x9 strip is impossible. Therefore, both 9s must be 3x3 squares. Placing the Green 3x3 at the top right and the Brown 3x3 at the bottom right anchors the eastern wall.

Squeezed between the two 3x3 squares is the Yellow 4. Horizontally, there are exactly 4 cells available (columns 5 through 8, row 4), forcing the Yellow 4 into a 1x4 horizontal bridge.

The left-middle section is now bounded. Columns 2 and 3 above the Peach 3 offer exactly 14 open cells (2 columns wide, 7 rows tall). The Purple 14 slots in flawlessly as a 2x7 rectangle. The remaining Teal 4, Red 3, and Light Blue 6 drop naturally into the remaining central columns to complete the puzzle.