Assume L 5, Q 15 primers on all Arts, L 3, Q 15 primer on Magic Theory, and Tractatuses of levels 6, 7, and 8 on two Arts, and a selection of Lab texts for spells, and Aura 3. I don't this is an unreasonable library. Assume teacher Com +1, Teaching 3, for teaching SQ 7. Assume student Int +1.
Assume that as long as the apprentice can benefit from his books the magus lets him read for 2 seasons each year, and uses him as a lab-slave for the other 2. When books are no longer available, assume the magus teaches for one season and uses the lab-slave for 3.
First year is an exception, as you need to open the Arts to claim the apprentice, and allow him to read up on magic theory to be able to use him in the lab.
Notation: Year.Season
1.1: Opening the arts.
1.2: Read primer on Magic Theory, gives MT level 3.
1.3: Lab, 2xp on MT.
1.4: Lab, total 4xp on MT.
2.1: Read primer on Art 1, gives Art level 5.
2.2: Read primer on Art 2, gives Art level 5.
2.3: Lab, total 6xp on MT.
2.4: Lab, total 8xp on MT.
...years 3-4 follow pattern...
5.1: Read primer on Art 7, gives Art level 5.
5.2: Read primer on Art 8, gives Art level 5.
5.3: Lab, total 18xp on MT.
5.4: Lab, total 20xp on MT, gives level 4.
6.1: Read primer on Art 9, gives Art level 5.
6.2: Read primer on Art 10, gives Art level 5.
6.3: Lab, total 2xp on MT.
6.4: Lab, total 4xp on MT.
7.1: Read primer on Art 11, gives Art level 5.
7.2: Read primer on Art 12, gives Art level 5.
7.3: Lab, total 6xp on MT.
7.4: Lab, total 8xp on MT.
8.1: Read tractatus Q 6 on Art 1, gives Art 1 level 6.
8.2: Read tractatus Q 7 on Art 1, gives Art 1 level 7.
8.3: Lab, total 10xp on MT.
8.4: Lab, total 12xp on MT.
9.1: Read tractatus Q 8 on Art 1, gives Art 1 level 8.
9.2: Read tractatus Q 6 on Art 2, gives Art 2 level 6.
9.3: Lab, total 14xp on MT.
9.4: Lab, total 16xp on MT.
10.1: Read tractatus Q 7 on Art 2, gives Art 2 level 7.
10.2: Read tractatus Q 8 on Art 2, gives Art 2 level 8.
10.3: Lab, total 18xp on MT.
10.4: Lab, total 20xp on MT.
11.1: Teaching Art 1, total 7xp.
11.2: Lab, total 22xp on MT.
11.3: Lab, total 24xp on MT.
11.4: Lab, total 26xp on MT, gives MT level 5, plus 1xp.
12.1: Teaching Art 1, total 14xp, gives level 9, plus 5xp.
12.2: Lab, total 3xp on MT.
12.3: Lab, total 5xp on MT.
12.4: Lab, total 7xp on MT.
13.1: Lab texts Art 1 + Art 2 with: 9 + 8 + 1 + 5 + 3 = 26 levels of spells.
13.2: Lab texts Art 1 + Art 2: total 52 levels of spells.
13.3: Lab, total 9xp on MT.
13.4: Lab, total 11xp on MT.
14.1: Lab texts Art 1 + Art 2 with: 9 + 5 + 1 + 5 + 3 = 23 levels, total 75.
14.2: Lab texts Art 2 + Art 3 with: 8 + 5 + 1 + 5 + 3 = 22 levels, total 97.
14.3: Lab, total 13xp on MT.
14.4: Lab, total 15xp on MT.
15.1: Lab texts Art 4 + Art 5 with: 5 + 5 + 1 + 5 + 3 = 19 levels, total 116.
15.2: Lab texts Art 6 + Art 7: total 135 levels of spells.
15.3: Lab, total 17xp on MT.
15.4: Lab, total 19xp on MT.
16.1: Gauntlet, teach Parma.
End result:
Magic Theory: 5, need only 11xp to reach 6.
Arts: one at 9, one at 8, all others at 5. Need 5 more xp for the Art at 9 to reach 10.
135 levels of spells.
I don't think that sounds weak for someone fresh off the gauntlet, especially considering that he has actually had only 2 seasons of teaching...
Looking at things like this, it becomes apparent that mages who use their Apprentices as manual labor are not going to have very competent apprentices compared to those who encourage their apprentices to read!
It seems also rather obvious to me, that there should be a reasonable bonus for having a teacher while you study from a book -- otherwise it really doesn't make sense to teach anything as long as there are books for the apprentice to read.
Also, "all arts at 5" is starting to seem more like a guideline for Gauntlet then taking apprentices...
Cheers,
--d