Cheryl's Birthday

The puzzle, originally set in the 2015 Singapore and Asian Schools Math Olympiad, know as Cheryl's Birthday, has generated a lot of interest over the past few weeks.

A discussion of the puzzle here queried the meaning of the term "day" in the statement "Cheryl then tells Albert and Bernard separtely the month and day of her birthday respectively".

The generlly accepted interpretation is that it is the day of the month, but I wondered whether the puzzle could be solved if "day" were interpreted as the day of the week, as suggested in the discussion.

The solution, assuming the "day of the month" interpretation, looks like this:

The days of the week associated with each date in 2015 are:

 

Now suppose Albert and Bernard are told all these dates, Albert is told the month of Cheryl's birthday and Bernard is told the day of the week. A solution can still be derived, as follows:

A solution with this structure would work for any other year, as the days of the week would all be offset by the same amount.