Number of starting learned 1st Level Spells for Wizard

[bazhil]

Hello,
According to the rules, a wizard learns a # of 1st level spells equal to 3 + Int modifier at level 1. Add to that the two spells you learn when you reach level 2, which can be nothing but first level spells, most people will have 5 + Int Modifier 1st level spells that they know.

My question is, I am starting a game at 10th level. My starting Int after racial modifiers was 19 (+4) but has been increased at 4th and 8th levels to 21 (+5). In addition, I purchased the Headband of Vast Intelligence +6 which gives me an Int of 27 (+8). My question is, how many 1st level spells do I know?

You could make a case that I know 13 (5 + 8). However, I did not have the 4th and 8th level ability score increases when I was level 1. Whether I had the Headband is less clear. It's possible it was an heirloom or something that I had at that level and my character started with.

What do you think?

Thanks in advance.

[Isil-zha]

The headband and the points from level ups do not count towards the free spells you know. But you can, of course, purchase more spells for your spellbook with the starting gold you get.

[Dorian 'Grey']

Correct. You would have 3+Int at 1st plus 2 more from 2nd=5+Int.

The other spells from leveling can go to any level you can cast at the time you gain them.

Also, if you are starting at level 10, then you will have plenty of 'time' and gold to scribe scrolls into your spellbook by purchasing them first.

You get 62,000 gp! (CRB p.399)