Difference between revisions of "2013 UNCO Math Contest II Problems/Problem 6"

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Revision as of 17:22, 19 October 2014

Problem

There is at least one Friday the Thirteenth in every year.

(a) What is the latest possible month in which the first Friday the Thirteenth can occur?

(b) In a year in which the first Friday the Thirteenth occurs in its latest month, what day of the week is January $1$?

The table below shows the number of days in each month. February has $29$ days in leap years and $28$ in others.

$\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline JAN & FEB & MAR & APR & MAY & JUN & JUL & AUG & SEP & OCT & NOV & DEC \\ \hline 31 & 28 or 29 & 31 & 30 & 31 & 30 & 31 & 31 & 30 & 31 & 30 & 31 \\ \hline \end{tabular}$


Solution

See Also