Mordenkainen's Private Sanctum, Teleportation Circle, and possibly other spells have text like:
You can create a permanent teleportation circle by casting this spell in the same location every day for one year.
The Dispel Magic has:
The DC is 10 + the spell's level.
Spell level can be increased by using higher level spell slot, and I see no requirements that spell to be permanent must be cast by the same caster every time. Storytelling-wise, it would then make sense to invite archmage with 9th level slots to perform first or last casting for stronger, harder to dispel effect, and use "apprentices" for day-to-day casting duty. But is it mechanically possible?
What dispel DC would such permanent circle or sanctum have, if spell slot level used would vary?
Best Answer
Difficulty to dispel depends only on level of the last casting
Teleportation circle has a duration of 1 round.1 That means each time you cast it, it lasts for about 6 seconds and then goes away completely.
The general rules for spell casting say that a spell ceases to exist after its duration has expired. Nowhere does this spell have text that overrides this rule. There is no way for a spell to have an effect outside its duration unless the spell specifically says there is. This spell does not say anything of the sort.
So, there is no way for the spell level of the other castings to have any effect on the permanent circle because those castings have all expired and are no longer having any effect.
Think of it this way, what level is the second to last casting? Obviously it is whatever level you cast it at. Do the previous castings have any bearing on how hard the spell is to dispel then? No, because only one casting is active. The same logic applies to the last casting except that that one happens to become permanent.
Thus, it would only be the last casting of the spell that determines the spell level of the circle because that is the only spell effect active at the time.
Bonus: this is also the simplest solution
Besides being the solution supported by the rules, this is also the easiest out of all the ways to calculate the difficulty to dispel the circle, which is great news for the DM and the players.
Being that it is only one number there is no calculation needed. Also, because it is the last of all the spells cast there are no numbers to remember. Taking the average (as an example of a houserule one might apply in lieu of the official method), would require the tracking, remembering, and calculation of 365 castings of the spell over a year of game time and possibly more than that in real-world time. That is a lot of numbers. Hope you don't lose the paper you wrote them all down on!
tl;dr On top of being the rules-supported solution, this solution also beats all other methods in terms of simplicity.
1 - Since all the spells have similar wordings I'm just going to focus on one of them but the same logic applies to all of them.