Holiday celebration and Primitive Roots

You say, "this question", but you show two unrelated questions.

Please ask about one problem at a time, and show what you have tried and where you are stuck, so we can know how to help.

You are not following the guidelines here, which are intended to help you get good answers more quickly.
 
I usually do not give a hint without seeing any work but this is a tricky problem. Ah you listed this under advanced math so my hint will be less clear.

If we number everyday of the year by 1,2,3,4,...?, then which days (in number) will be the 10th of each month?

For the entire year, what days (in number) will be Wednesdays?

If you answer both questions above what do you do with these two answers to solve your problem?
 
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