A given month has $$31$$ days, and it has four Mondays and four Thursdays. What day of the week is the $$20^{\rm th}$$ of this month? 
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It implies that there are four Mondays, four Tuesdays, four Wednesdays, and four Thursdays. Similarly, there are five Fridays, five Saturdays, and five Sundays. The first day of the month therefore must be a Friday. $$20\div7=2\text{ R }6$$. The $$20^{\rm th}$$ day of this month is a Wednesday, which is the $$6^{\rm th}$$ day after Friday, inclusive. 