You have a club that meets the fourth Thursday of each month, and another one that meets the last Thursday of each month. Usually you have to choose to attend one meeting or the other as the fourth Thursday of the month is usually the last Thursday of the month. However, some months have five Thursdays. In those months you can attend both meetings.

Develop an algorithm to find all the fifth Thursdays of those months that have them, and set it to calculate them for ten years. You are given subroutines that convert Gregorian calendar dates to and from JD numbers, which are the number of days a given date is past a certain fixed date in the distant past (more than 6000 years ago). You also have a 2003 calendar available that tells you Jan. 2, 2003 was a Thursday.

There are at least 52 Thursdays in a year, every month has at least 4 Thursdays. Then, there are at least 4 (52 - 12 * 4) Thursdays which occur as the 5th Thursday of a month.

*Edited on ***October 7, 2003, 2:54 pm**