Genshin Impact : Philosophies of Ingenuity

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To obtain Philosophies of Ingenuity, you need to challenge the Domain of Mastery: Witticism on level four at the Steeple of Ignorance Domain in Sumeru.

The game recommends your party level be 88+ to challenge Domain of Mastery: Witticism IV. It is only available on Tuesdays, Fridays, and Sundays. To claim the rewards, you'll need to spend 20 Resin or use a Condensed Resin to receive double. You do not have to claim the rewards if you choose not to do so.

You may not always receive Philosophies of Ingenuity when you complete this domain, but you will always receive Teachings and Guides to Ingenuity that you can use to create Philosophies of Ingenuity at a crafting station.

Check the image below for the Domain's exact location:

Talent Level-Up material. Ingenuity is the leaf-veins of the nation of wisdom. Ingenuity is completed by harmonious conduct. What is done completes what is thought. Wisdom blooms where the mind, words, and practice converge.