Need a program to make a scheduled for a Korean school

Factual Questions
1

{Title Edit} Need a program to make a schedule for a Korean school.

We foreign teachers (aka “Guest English Teachers” [GET]) in South Korea’s public schools operate under a system employing a Korean teacher of English, known here as the co-teacher (CT). The GET is required to have a CT in the classroom during each lesson. Each school has one or more, usually more, CTs. The fun thing is that nobody knows what the CTs’ schedules will be until a couple of days into the first semester (which begins on 2 March). Once those schedules are fixed, then the GET can make his schedule. From experience, I know this is a royal pain to do “by hand.” What I would like is to have a simple program to do this with the following parameters:

[ol][li]Each class (elementary school has six grades, middle school has three grades, and high school has three grades) has three English periods per week.[/li][li]The CT attends all three periods, but only teaches two of the periods.[/li][li]The CT’s schedule includes classes on Saturday mornings (only the second and fourth Saturdays are School off-days). Saturday morning classes are first through fourth periods.[/li][li]The GET’s schedule must be for 22 teaching periods per week or less. (But see Paramter 6.)[/li][li]The GET is to meet every class in the school once every week. (But see Paramter 6.)[/li][li]The program must have the option of the GET meeting all the classes in only one grade once every other week, instead of once every week, if the school has more than 22 classes.[/ol][/li]
So, what I’d like is to input the following:

[list=a][li]CTs’ schedules (identify the CTs either by name (bonus if possible to do in Hangul) or by number).[/li][li]School level (elementary, middle, or high school)[/li][li]Number of classes for each grade.[/list][/li]
And then the program would output all the possible schedules, including those which would have the GET meeting one grade only every other week.

Every GET in South Korea will owe you a million thanks if you can hook us up with this before the end of February!

Why the rush? Well, once the CTs’ schedules are fixed, that’s the very day we GETs are supposed to start teaching by our new schedule, giving us approximately five to twenty minutes to come up with said schedules. Just for fun this year, I’d like to avoid the madness.

It would be great if someone knows of a free downloadable program or a free online site that will do the work, too.

2

I left out two paramaters:

  1. The school week is Monday through Friday, except that mornings of the 1st, 3rd, and 5th Saturdays of the month are also school days.
  2. The GET only works Monday through Friday.

Again, thanks to anyone who can help!

3

So the GET has to CT the middle school every other week but only on the 5th Monday of odd-numbered months in leap years with fewer than 19 classes…? :eek:

Um… there are websites like Doodle.com that can help with these things, but they’re usually meant for less, well, demonic schedules. I’d love to see if something like this actually exists or can be made without losing one’s sanity.

4

It really does sound like a bad round of Fizzbin, doesn’t it? For the past five years (which is ten rounds, given that there are two semesters per year), I’ve spent more than a few hours at home with a pack of index cards spread on the floor. I really don’t want to do that kind of old-school scheduling again.

The doodle site seems to be good for reunions and the like and, as you say, not the demonic set-up in the OP.