Today is the 30th day of the 5th month of the year, and also the 150th day of the year. If you multiply the day of the month (30) by the number of the month (5), the result is the number of days in the year so far (150).

How rare an event is this? Is this something we can say is true for many days of the year? Obviously it is true for all 31 days in the month of January, but that’s a sort of degenerate case.

Not counting January, how many days in the year have this unusual numerical property?

Hint: 5/30 is the last time this is true this year, and next year we’ll experience the last instance before May.

Thank you for taking a most excellent logical leap!