Ran and Yukari

Yukari Yakumo is a legendary youkai who is able to manipulate boundaries. She is the master of Ran Yakumo. Yukari is called the "gap youkai" although "gap youkai" is not the name of a species, as she is more of a one-of-a-kind type of youkai. Regardless of her power, Yukari appears to be the most well-informed being in Gensokyo of any kind and usually achieves her goals through manipulating events rather than direct combat.

Yukari is known for being a very youkai-like youkai who sleeps all day and lives for the enjoyment of life. Though she rarely leaves her house, Yukari is well-connected and is acquainted with most of the most powerful youkai as well as anyone having anything to do with the Great Hakurei Barrier or the outside world, although Yukari rarely attacks humans. Yukari has a tendency to toy with her opponents rather than use her full power from the start. If anyone is suited for the role of "mastermind", it's Yukari. Yukari excels at mathematics and is experienced due to her long life.

Yukari possesses superhuman intellect and especially surpasses in dealing with numbers. In Bohemian Archive in Japanese Red, as Ran Yakumo said, this intellect is something that even Ran is not able to understand, to the extent that for example that Yukari is able to determine the depths of the darkness of Avici or determine in an instant how long it would take for Ursa Major to devour the North Star, as it seems. Concretely to what extent this amazing intellect goes is hard to know, but it would be no mistake to think that this intellect far surpasses that of humans.

Yukari often has a great deal of insight and understanding about whatever happens in Gensokyo, and possesses considerable intellectual prowess, as well. Though Yukari seems flaky and unreliable most of the time, when the safety or security of Gensokyo is at stake, she won't hesitate to get involved, even if it means using others to do the work for her. For example, in Scarlet Weather Rhapsody, Yukari treats Tenshi Hinanawi with much hostility after finding out the plot of the Heavens. Yukari could easily be either a villain or a heroine, depending on her whims.

Yukari deals with problems by manipulating others to act to resolve things for her. Yukari seems to rarely act directly except in particularly egregious situations. In all cases, Yukari rarely lets anyone know what her true aims or goals are and sometimes these goals are extremely abstract. Yukari has a well-deserved reputation of being fickle, whimsical and lying often and thus many characters in Gensokyo dislike her. For whatever reason, Yukari takes it all in stride and does not seriously deny any of those comments. Yukari seems to actively try to keep her more obviously-altruistic actions a secret, such as her donations to the Hakurei Shrine in Strange and Bright Nature Deity. Yukari possibly cultivates this image to ensure that people continue to fear her as a youkai, as this is what her true goal for a particularly complex gambit is revealed to be at the end of Cage in Lunatic Runagate.

Ran is described as a gentle youkai, unless provoked which she then becomes angry and domineering. Although Ran is a shikigami, she sometimes "forgets" her position as a servant and acts of her own volition.

Ran is an extremely strong shikigami, to the point that she can use shikigami of her own. Her shikigami, Chen, only possesses the wisdom of a child, implying that Ran lacks the level of power that Yukari has with respect to shikigami. While Ran cannot act against Yukari's orders, Chen is capable of disobeying Ran. Because of this, Ran sometimes has to lure or manipulate Chen with catnip.

Ran has super-human intellect equal to that of Yukari's, and excels at mathematics. According to Bohemian Archive in Japanese Red, she was able to formulate and prove an equation for figuring out the width of the Sanzu River. The shikigami of Gensokyo have been often likened to personal computers found in the outside world.