In a month of 31 days there will be 4 dates where the same day of the week falls on that date if d+28>31, so d>3 where d is the earliest date in the month. So, for example, if d=4, then the dates are 4, 11, 18, 25. Also, d<8, because if d=8, then there would be an earlier date, d=1. Therefore, 3<d<8. We can also write 3-3<d-3<8-3, that is, 0<d-3<5. If d represents a Monday, then d-3 represents Friday, so 0<F<5 and 3<M<8 for the Friday and Monday dates. This gives us F=1, 2, 3, 4 and M=4, 5, 6, 7. But for 4 Fridays F must be greater than 3, which leaves F=4 and so M=7 and the first day of the month must be Tuesday. This gives us F=4, 11, 18, 25 and M=7, 14, 21, 28.