[seivan]

I might have missed something here, but I think your explanation for the second "instruction" isn't exactly valid.

# now B knows-- cut dup days

You're not removing duplicate days. You're removing months that contained "days occurring once".

Because A knows: B doesn't know. Which means A knows it's not on May and June -the only months containing "days occurring once.

I solved it this way (in my head).

#MONTH doesn't know and knows DAY doesn't know

Remove "all days occurring once"

Remove "months that contained single occurrence days"

#DAY didn't know, but knows now.

Remove "duplicate days"

#MONTH knows now.

Remove "Months with more than 1 day"

Leaving July 16. :-)