A very special type of polysquare puzzles is the set of 'square-puzzles', where all given shapes are squares with integral sidelength.
Reference
... Clinton (162) Charles C. Pinckney[?] 14 Federalist Rufus King (14) Other elections: 1792, 1796, 1800, 1804, 1808, 1812, 1816 Source: ...