Question #1
Show that every year most have at least one month and at the most three months that have a Friday the 13th
Here is a link to my spread sheets that have seven years with each year starting on a different day of the week
Years starting with Sunday, Monday, Tuesday
Years starting with Wedsday, Thursday, Friday
As you can see every year has at least one Friday the 13th, and at most they have three Friday the 13ths. I used Red to show Friday the 13th and blue to show Friday the 13ths if the year was a leap year.
Question #2
Any year that starts on a Thursday and is not a leap year will have a Friday the 13 in February and March, you can see this by going here
This would happen in 2004 but that is a leap year so this wont happen until 2009.
We know that every four years is a leap year. so that pushes the day a year starts back by one day. In 2004 the year starts on Thursday but that is a leap year so the next year starts on Saturday instead of Friday. 2008 starts on a Tuesday, but it is a leap year so thats why 2009 starts on Thursday and is not a leap year and therfor has a Friday the 13 in February and March