The Ryser formula expresses the permanent of an 
matrix,
where 
is a positive integer, as
 |
where the sum is over all subsets of 
, and 
is the number of elements in 
. The formula can be optimized by picking the subsets
so that only a single element is changed at a time (which is precisely a Gray
code), reducing the work per term from 
to 
.
The label of the disk moved at the 
th step in the standard optimal three-rod tower
of Hanoi solution is the element changed at the 
th transition of the binary reflected Gray
code ordering of these subsets (Gardner 1988b; Vardi
1991, p. 111).
