  B. D. Acharya has conjectured that if $\bigl(A_i: i=1, 2, ...,
2^{|X|}-1\bigr)$ is a permutation of all nonempty subsets of a set $X$ with at
least two elements such that for each even positive integer $j<2^{|X|}-1$,
$A_{j-1}\triangle A_j\triangle A_{j+1}=\emptyset$, then $|X|=2$. In this
article, we show that if the cardinality of a set $X$ is more than four, then a
permutation as described above indeed exists.
