  Burke and Teng introduced a two-player combinatorial game Atropos based on
Sperner's lemma, and showed that deciding whether one has a winning strategy
for Atropos is PSPACE-complete. In the original Atropos game, the players must
color a node adjacent to the last colored node. Burke and Teng also mentioned a
variant Atropos-k in which each move is at most of distance k of the previous
move, and asked a question on determining the computational complexity of this
variant. In this paper, we answer this question by showing that for any fixed
integer k (k>=2), Atropos-k is PSPACE-complete by reduction from True
Quantified Boolean Formula (TQBF).
