Looking at the "current month" question as a mathematical problem, let us assume that the current month is (b). The only wayit can work is if last month (a) had 31 days and ended on Monday (i.e. Mon 31st), and next month (c) starts on Friday, giving Thursday 7th.
That means that the current month (b) starts on a Tuesday and ends on a Thursday, so it must be a 31-day month. So was last month (a). The current month (b) can only be January or August to give two 31-day months in succession.