In a magical realm, there's a mysterious room called the Chamber of Perspectives. The room has a unique property: whoever stands at the center can see everyone else in the room, but cannot be seen by anyone. Conversely, if someone stands against any of the walls, they can see only the person at the center but not any other person standing against another wall. There are four uncommon friends - Dakarai, Eirlys, Mirembe, and Jiro. They decide to explore this room together. They enter the Chamber of Perspectives, and Dakarai heads to stand at the center while Eirlys, Mirembe, and Jiro each choose a different wall to stand against.

Mirembe, who is an avid lover of riddles, proposes a game: she asks Dakarai to close his eyes and guess the exact position of the other three without moving, only by using the logic of their spoken clues. Eirlys, standing against the north wall, says, "I can see the person at the center." Jiro, who is at the east wall, announces, "I can also see the person in the middle." Mirembe, from the west wall, states with a smirk, "Well, I can see Eirlys." Given these clues, how does Dakarai figure out where Eirlys, Mirembe, and Jiro are positioned without opening his eyes or moving from the center?
Dakarai knows the magical property of the Chamber of Perspectives and uses it to solve Mirembe's riddle. First, he reasons about Eirlys's statement that she can see the person at the center. This is true for anybody standing against one of the walls, so Eirlys's statement doesn't reveal anything about her exact location. The same reasoning goes for Jiro's statement that he too can see the person in the middle.

But Mirembe's statement gives away a crucial piece of information. Since anyone against the wall can only see the person at the center, the fact that Mirembe claims to see Eirlys explicitly violates the room's magical property. This contradiction suggests that Mirembe is not standing against a wall as she would be unable to see Eirlys.

Dakarai figures that Mirembe is teasing her friends by trying to trick them because there is no way for her to see Eirlys if she were truly against one of the walls. Given that Mirembe enjoys riddles, Dakarai considers that her statement may only make sense from her perspective if she is not where she claims to be. He suspects that she might not be against a wall at all, but rather somewhere else where she might catch a glimpse of Eirlys. Yet, this doesn't align with how the magic of the room works.

Meanwhile, Dakarai considers the layout of the room and the nature of Mirembe's clue. If he assumes that everyone else is being truthful about being against a wall while he's in the center and invisible, then the only way Mirembe could "see" Eirlys is if she is inferring Eirlys's position based on Dakarai's orientation or other subtle cues he might be offering, possible only because she knows the room's properties well. Dakarai, familiar with his friends, recalls Mirembe's playful nature, and it strikes him that she might have spoken metaphorically: maybe she meant she knew where Eirlys was positioned rather than actually seeing her with her eyes.

With this in mind, Dakarai deduces that Eirlys and Jiro are telling the truth and standing against the north and east walls, respectively. Both have followed the agreed rules and simply stated facts afforded by the Chamber's magic. Mirembe, being witty and clever with words, would choose the only remaining wall opposite Eirlys - the west wall - to make a statement that seemed physically impossible but was logically sound once deciphered.

Thus, without opening his eyes, Dakarai concludes that Eirlys stands against the north wall, as Jiro's unremarkable clue doesn't provide any clues about their relative positions. Jiro must be standing against the east wall for the same reasons. And Mirembe, with her tricky clue, has revealed that she has positioned herself against the west wall, the only place she could be to make such a statement referring to Eirlys's position, which she has inferred but not actually seen.

Therefore, Dakarai confidently names the positions of his friends: Eirlys is on the north wall, Jiro is on the east wall, and Mirembe, despite her misleading clue, is on the west wall.