Here, uniqueness is up to symmetry.
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This puzzle includes given pieces and makes good use of absent tiles:
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Acknowledgements and Changes
2023-03-26 Thanks to Karoo for feedback on this genre (symmetric solutions are preferable; pawn to cross)
2023-12-22 A highlighting error due to absent tiles found by PinkHoodie was fixed, and a puzzle by this author was added! Also, the aux markers were corrected.
2025-01-03 Encoding Chess Loop was fully reencoded to use piece-counts instead of parameters