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When this puzzle was originally published I solved it in Perl using an exhaustive search, but it took about 30 minutes to run.

Here’s the search recoded in Python, with a couple of modifications to reduce the run time. It finds a number of maximal length solutions in 2.0s (running under PyPy).

It might be faster to assemble the numbers into chains, and then assemble non-intersecting chains into a ring.

Solution:The maximum number of digits in the ring is 64.