How to make a school timetable without clashes

Write down the constraints before touching the grid

You need three lists. None of them takes long, and every clash you will find later comes from something missing here.

• The school day: how many periods, how long, where the breaks fall, and whether Friday or Saturday is shorter.
• Each class: every subject and how many periods a week it gets.
• Each teacher: what they teach, to which classes, and any days or periods they are not available.

Check the arithmetic

Take an example week of seven periods Monday to Thursday and five on Friday. That is 33 slots. The subject loads for every class must add up to exactly 33. If Class 6 comes to 35, no arrangement will ever work, and it is much better to find that out now than on the third evening of trying.

Do the same for teachers. Add up every period each teacher is assigned. Anyone over the number of slots in a week is impossible. Anyone within two or three of it will be teaching without a free period for days on end.

Place the hardest pieces first

Some periods have very few places they can go. Put those on the grid before anything else:

• Teachers shared between many classes, or between the boys' and girls' sections.
• Part-time and visiting teachers who come in on fixed days.
• The computer lab and science labs, which one class at a time can use.
• Double periods for practicals.

Rules that keep it fair

With the fixed pieces placed, fill in the rest with a few rules. Keep the same subject to one period a day for each class unless it is a planned double. Put mathematics and languages in the morning where you can. Do not give any teacher more than four periods in a row. These are preferences, not laws, and a timetable that breaks one of them in two places is still a good timetable.

Find the clashes before term starts

The clash that matters is one teacher in two rooms in the same period. On paper it hides, because each class timetable looks fine on its own. The check is to turn the grid around: write out each teacher's week from the class timetables and look for any period with two entries. Do the same for each lab.

Give teachers their own timetables a week before term and ask them to check. The teacher who takes Class 7 and Class 9 for science will spot a clash in ten seconds that took you an hour to miss.