Oyler,
I have nothing but admiration for anyone who sets a Listener, particularly the numericals. How anyone can even contemplate the task is beyond me. However, the test of any puzzle lies in the reaction of those who attempt to solve it, not in the pedigree of the setter. Even Euripides didn't write top notch dramas every time, and, sad to say, many of us felt this puzzle was below standard. I could not see anything in the way of deductions or reasoning - I am no mathematician, so could have missed the nuances - and solved this by the simple expedient of finding a starting point and calculating the options. Brute force from a brute. As I intimated above, I almost found the process dull enough to fail to complete. No offence intended to anyone, but this was not the fine dining we have come to expect.