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2013 UNCO Math Contest II Problems/Problem 6

Revision as of 15:12, 16 October 2014 by Timneh (talk | contribs) (Created page with "== 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 yea...")
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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

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