Its much more efficiently solved with the naive 'represent the distance between each adjacent ring as a number' and slide the array of numbers representing the

Its much more efficiently solved with the naive 'represent the distance between each adjacent ring as a number' and slide the array of numbers representing the sample along the known line and for each possible offset, calculate the error. Then you're left with some shortlist of candidate dates and their probabilities. It reminds me of the algorithms for locating reads on the genome.