Anthony Edwards has produced an elegant representation of the genetic code in all its degenerate complexity for this month's , cover explained in Touching Base. Now you have a chance to use his device to solve a puzzle. Please post your solutions to the Nature Precedings website, or send them to me and I'll add them to this blog.

Problem: Find a ‘Gray code’ order for the codons.
When the numbers 1 to 2n are written in binary form in their natural order the number of digits, 0 or 1, that change on proceeding from one number to the next varies. There exist, however, orderings in which only a single digit changes each time and the last number only differs from the first in respect of a single digit as well. These are known as Gray codes, the numbers forming a complete cycle.
The same principle can be applied to the codon triplets, ordering all 64 in a cycle such that each differs from its predecessor in exactly one position. There are many such orders, each forming a Gray code. They differ in the extent to which they group together triplets that code for the same amino-acid.
One measure of success in forming such groups would be the number of times in the cycle that neighbouring triplets code for different amino-acids (or a stop signal). Since there are 21 of these the absolute minimum of such changes between neighbours is simply 21, but this may not be attainable.
It is easy to find a Gray code ordering with 25 changes by threading a regular route through the standard table of the genetic code. But can you find one with fewer? There’s a route through the Edwards–Venn diagram given in Figure 3 of ‘Picturing the genetic code’ (Nature Precedings doi:10.1038/npre.2007.682.1) with only 23 changes of amino-acid.

P.S. Why ARE there two groups of serine codons, anyway?