We extend the study of the 2-Solo Chess problem which was first introduced by Aravind, Misra, and Mittal in 2022. 2-Solo Chess is a single-player variant of chess in which the player must clear the board via captures such that only one piece remains, with each piece capturing at most twice. It is known that the problem is solvable in polynomial time for instances containing only pawns, while it becomes NP-complete for instances restricted to rooks, bishops, or queens. In this work, we complete the complexity classification by proving that 2-Solo Chess is NP-complete if the instance contains only knights or only kings.

翻译：我们扩展了Aravind、Misra和Mittal于2022年首次提出的两人单人国际象棋问题的研究。两人单人国际象棋是一种单人变体，玩家必须通过吃子清空棋盘，使得仅剩一枚棋子，且每枚棋子最多吃子两次。已知若实例仅包含兵，则该问题可在多项式时间内求解；若实例限制为车、象或后，则问题变为NP完全。本文通过证明当实例仅包含骑士或仅包含王时，两人单人国际象棋为NP完全，从而完成复杂度分类。