# Math Help - Problem solving

1. ## Problem solving

Peter and John work as cashiers at a Department store in Marawi City that is open 7 days a week. Peter works for 2 days and then has a day off. John works for 4 days and has 2 days off. On Wednesday, November 1, an official Holiday, neither Peter nor John worked. Peter worked on November 2, and John reported to work on November 3.On what days in November, aside from November 1, do both Peter and John have off?

Please, can anyone have the idea on how to solve this problem?
Thank you so much!

2. Is this a geometrical problem?

The easiest thing is to make a table like this.

$\begin{array}{lcccccccccccccccc}
\mbox{Date} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15 & \dots\\
\mbox{Peter} & X & X & & X & X & & X & X & & X & X & & X & X & \dots\\
\mbox{John} & & X & X & X & X & & & X & X & X & X & & & X &\dots\\
\end{array}$

The problem would be clearer if it did not mention the official holiday. As it is, it opens a possibility that Peter's day off was the last day of October and he should have worked on November 1 if it were not for the holiday. Then, according to his regular schedule, his next day off is November 3. I ignored this possibility and assumed that Peter and John would have November 1 off even without the official holiday.