Four cylindrical drums, each of radius 1 m, are placed such that each one touches other two drums. A sewer pipe is to be placed through the gap of these drums. What could be the maximum possible radius for this pipe?

When four cylindrical drums of radius 1 m are placed such that each touches two others, their centers form a square with a side length of 2 m. The diagonal of this square passes through the centers of two diagonally opposite drums and the gap in the middle. The length of this diagonal is calculated as side × √2, which equals 2√2 m. This diagonal consists of the radius of the first drum (1 m), the diameter of the sewer pipe (2r), and the radius of the second drum (1 m). Therefore, 2√2 = 1 + 2r + 1, which simplifies to 2√2 = 2 + 2r. Dividing by 2 gives √2 = 1 + r, leading to r = (√2 - 1) m. This represents the maximum possible radius for the pipe to fit exactly in the central gap between the four drums.