Katie's Perfect Gem
After the Library opens up on University (day 12, at the Evoker lecture), you'll find the Quartermaster there. He's able to sell you gems, but if you say that you need a special Fire Gem for a special girl, he'll offer to sell you a Fire9 (A True Flawless gem, so the highest grade) after day 20. You can't use it yourself, but you can give it to Katie at the Gym. The gem will cost you 500 pounds, though.