Balanced Gray Codes

It is shown that balanced n-bit Gray codes can be constructed for all positive integers n. A balanced Gray code is one in which the bit changes are distributed as equally as possible among the bit positions. The strategy used is to prove the existence of a certain subsequence which will allow successful use of the construction proposed by Robinson and Cohn in 1981. Although Wagner and West proved in 1991 that balanced Gray code schemes exist when n is a power of 2, the question for general n has remained open since 1980 when it first attracted attention.