I am playing a level 10 alchemist, and because alchemist needs as much as he can for int (bombs per day, bomb's damage, craft alchemy, etc.), i want to maximize it. I need the cheapest items i can get, as i almost have no money, as well i need it to well. Any extracts that can do that is great too. As well feats and discoveries.
Headbands of Vast Intelligence, Tomes of Clear thought, and Races that grant a bonus to intelligence are the most common boosts to intelligence.
The headbands cost 36,000gp for +6 Enhancement Bonus to intelligence, but only 18,000 if you happen to have someone in your group with access to Craft Wondrous item and Fox's Cunning. You don't need access to Fox's Cunning if you take a +5 Penalty to the crafting DC. Tomes of Clear thought are exorbitantly expensive 137,500gp for a +5 Inherent Bonus.
Races that get a +2 Racial bonus to intelligence are:
- Blues (From Psionics Unleashed)
There are a number of methods, many already listed, to boost Intelligence.
Here are a few, some that are extreme longshots(As in GM FIAT only with no way for PCs to normally obtain):
Headband of Vast Intelligence +2/+4/+6(or variants such as Headbands of Aerial Agility, Mental Prowess, Mental Resilience, Mental Superiority, Ponderous Recollection, Shifter's) Type: Enhancement
Tome of Clear Thought 1-5 Type: Inherent
Ioun Stone(Scarlet and blue) Type: Enhancement
Stat Increase at levels 4, 8, 12, 16 and 20 Type: Untyped
Spells/Extracts are useful for damage and in the form of Crafter's Fortune Craft Alchemy checks
Racial Bonuses, See Sandwich's answer.
Template adjustments such as Advanced, Half-Celestial/Dragon/Fiend, Fey Creature, Foo Creature, Nightmare Creature, Animal Lord Type: Untyped
Racial adjustments, such as finding a Vampire to turn you. A jiang-shi is superior to a western vampire for Intelligence boosting purposes. Type: Untyped
Summoning either a Contract Devil(and making a contract with such) or a Succubus and convincing them to grant you their Profane Gift Type: Variable(At GMs discretion for Contract, of Profane for Succubus)
Leadership feat to get an item cohort take the perfection advancements for inherent up to +5 INT
The standard intelligence-boosting items and methods are as follows:
- Headband of Vast Intelligence (+6 Enhancement Bonus)
- Tome of Clear Thought (+5 Inherent Bonus)
- Stat increase at level 4 and every 4 levels thereafter (+5 Untyped Bonus)
Additionally, as an Alchemist, you can either take the Cognatogen discovery or the Mindchemist archetype to get an ability that essentially is like Mutagen for mental stats. Through this ability, you can get up to a +8 alchemical bonus to your Intelligence for 10 minutes per Alchemist level.
Please see @Sandwich's answer to get a detailed like of Int-boosting races.
1) The custom magic items price guidelines are explicitly to be followed exactly when crafting attribute boosting ion stones, even by a very conservative reading. The formula is
(bonus squared × 1,000 gp × 2)
which makes your attribute scores, including int, limited only by your access to gp. As a member of a level 10 party, you should have access to vast quantities of gold via things like Fabricate, scrolls of Polymorph Any Object, etc and the exact amount will depend on if you have a rogue in the party and, if not, how much time your wizard is willing to spend making you gp. Based on experience, you'll probably end up limited more by time than gold, here, unless you have a rogue in which case the bonus is essentially arbitrary.
Unfortunately, in WBL (wealth-by-level) games all your 62000 gp would only net you +5 via this method (+6 if you took any crafting feats), which is very lackluster for the investment.
2) In a WBL game, the Headband of Intellect provides one of the cheapest sources of long-term int boosting, but caps out at +6, while the Crimson Sphere Ion Stone caps out at +12 if the second method of Resonant Power determining is used, but is much more expensive. A flawed Scarlet and Blue Sphere Ion Stone with the right resonant power will give you +4 Int but -2 Con for 6500, which includes the cost of a wayfinder. A Dull Gray Stone with the right resonant power can grant +2 Int for 525 gp. This last option provides the very best gp/bonus return available, but is generally insufficient for a 10th level character. The +4 int -2 con is probably what you want at level 10, especially since you have lots of access to physical buffs as an alchemist.
This answer assumes you already have a 10th level character and are trying to optimize for that character, and neglects both the cost of purchasing the right resonant power (~0-1250 gp for a dull gray, ~0-300000gp for a scarlet and blue sphere) and the potential for multiple resonant powers on a singe stone (technically you can get +8 int from a roll of 93-04-04-04 on a Scarlet and Blue Sphere, with a 1:100000000 chance if truly random).
Two so-far unmentioned methods:
Ageing effects, middle aged or higher can get you +1 to Int. (Along with the other mental stats, at a cost of physical stats)
Also technically levels Dragon Disciple would increase it, but it's a terrible return on investment! (i.e. for the sake of the +2 intelligence boost alone)
The Alchemist's Cognatogen is probably one of the best returns on investments though when your budget is 200gp.