The February of a given year has five Fridays. What day of the week was January $$31$$\textsuperscript{th~}of that year? 
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There are seven days in a week. In order to have five Fridays, a month has at least $$4\times 7+1=29$$ days. Since February has at most $$29$$ days, the $$1$$\textsuperscript{st} and $$29$$\textsuperscript{th} days of this February must be Friday, which means that January $$31$$ is Thursday. 