Let S ( n ) S(n) be a collection of subsets of { 1 , . . . , n } \{1,...,n\} . In this paper we study numerical obstructions to the existence of orderings of S ( n ) S(n) for which the cardinalities of successive subsets satisfy congruence conditions. Gray code orders provide an example of such orderings. We say that an ordering of S ( n ) S(n) is a Gray code order if successive subsets differ by the adjunction or deletion of a single element of { 1 , … , n } \{1,\ldots ,n\} . The cardinalities of successive subsets in a Gray code order must alternate in parity. It follows that if d ( S ( n ) ) d(S(n)) is the difference between the number of elements of S ( n ) S(n) having even (resp. odd) cardinality, then | d ( S ( n ) ) | − 1 |d(S(n))| - 1 is a lower bound for the cardinality of the complement of any subset of S ( n ) S(n) which can be listed in Gray code order. For g ≥ 2 g \ge 2 , the collection B ( n , g ) B(n,g) of g g -blockfree subsets of { 1 , … , n } \{1,\ldots ,n\} is defined to be the set of all subsets S S of { 1 , … , n } \{1,\ldots ,n\} such that | a − b | ≥ g |a-b| \ge g if a , b ∈ S a,b \in S and a ≠ b a \ne b . We will construct a Gray code order for B ( n , 2 ) B(n,2) . In contrast, for g > 2 g > 2 we find the precise (positive) exponential growth rate of d ( B ( n , g ) ) d(B(n,g)) with n n as n → ∞ n \to \infty . This implies B ( n , g ) B(n,g) is far from being listable in Gray code order if n n is large. Analogous results for other kinds of orderings of subsets of B ( n , g ) B(n,g) are proved using generalizations of d ( B ( n , g ) ) d(B(n,g)) . However, we will show that for all g g , one can order B ( n , g ) B(n,g) so that successive elements differ by the adjunction and/or deletion of an integer from { 1 , … , n } \{1,\ldots ,n\} . We show that, over an A A -letter alphabet, the words of length n n which contain no block of k k consecutive letters cannot, in general, be listed so that successive words differ by a single letter. However, if k > 2 k>2 and A > 2 A>2 or if k = 2 k=2 and A > 3 A>3 , such a listing is always possible.