Two walls and a ceiling of a room meet at right angles at a point P. A fly is in the air 1 m from one wall, 8 m from the other wall and 9 m from the point P. How many meters is the fly from the ceiling?

1. **Set up the mental grid:** Just like the 2016 question where we visualize a grid starting from (0,0) [3], here we visualize the room corner 'P' as our origin (0,0,0).\n2. **Map the coordinates:** The fly's position is defined by its distance from the three perpendicular planes (walls and ceiling). We are given: \n - Distance from Wall 1 = 1 m (let's call this x)\n - Distance from Wall 2 = 8 m (let's call this y)\n - Distance from Ceiling = ? (let's call this z)\n3. **Apply the Distance Logic:** We are given the total straight-line distance from the origin P is 9 m. Previous years' analysis [16] tells us that perpendicular distances form a relationship where the square of the total distance equals the sum of squares of individual components. In 3D: $Total Distance^2 = x^2 + y^2 + z^2$.\n4. **Calculate:** \n - $9^2 = 1^2 + 8^2 + z^2$\n - $81 = 1 + 64 + z^2$\n - $81 = 65 + z^2$\n - $z^2 = 81 - 65$\n - $z^2 = 16$\n5. **Final Result:** $z = 4$. The fly is 4 meters from the ceiling.