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I needed both clues to solve this, though in retrospect I should have been able to solve it with just the first clue. Spoiler I experimented with placements of the large piece along edges and...
#1: Initial revision
I needed both clues to solve this, though in retrospect I should have been able to solve it with just the first clue. <details> <summary>Spoiler</summary> <!-- An empty line is required for markdown to render --> I experimented with placements of the large piece along edges and corners without success (that leaves the wrong size spaces to be filled along the rest of those edges), so I had already concluded that a large piece needed to not touch any edges. I failed to realize, though it is obvious in retrospect from the mathematical clue, that there must be exactly two large pieces (no other number allows all the space to be filled). A "floating" placement of one large piece allows two of the smaller pieces to pad out a six-square side. The additional clue that helped me was "symmetrical".  </details>
