Uniform-budget solo chess with only rooks or only knights is hard

Abstract

We study the Solo-Chess problem which has been introduced in [Aravind et al., FUN 2022]. This is a single-player variant of chess in which the player must clear all but one piece from the board via a sequence captures while ensuring that each piece performs at most as many captures as its budget allows. The time complexity of finding a winning sequence of captures has already been pinpointed for several combinations of piece types and initial budgets. We contribute to a better understanding of the computational landscape of Solo-Chess by closing two problems left open in [Aravind et al., FUN 2022]. Namely, we show that Solo-Chess is hard even when all pieces are restricted to only rooks with budget exactly 2, or only knights with budget exactly 11.