One fish per ten thousand cubic metres times the whole ocean gives 130 trillion, and the arithmetic is exact. The error is that a density you can picture is a surface density, and confining it to the 200 metre sunlit layer drops the figure by a factor of 18. A second chain built from the annual catch, which touches no ocean geometry at all, lands in the same decade, and that agreement is the result rather than either set of digits.
Dividing the cabin by the ball gives 29.8 million, which is exact arithmetic on the assumption that spheres tile space. They do not, and the correction is pinned on both sides by constants: a plain cubic grid anyone can build holds exactly 15,625,000 balls, and no arrangement whatever beats pi over root eighteen, which caps the count at 22.1 million. The answer is that interval, with a settled pour at 19.1 million sitting inside it.
Two people arrive at random inside the same hour and each waits fifteen minutes, so the reflex answer is a quarter. Drawing both arrival times as one point in a 60 by 60 square turns the question into an area, and the two corner triangles it leaves out have legs of 45, giving 7/16 rather than 1/4. The general formula n(2T-n)/T squared shows why the first minutes of patience buy the most.
A boat carrying a dense rock floats in a pool; the rock goes over the side and sinks. The mass inside the pool is unchanged, so the reflex says the level cannot move, but it falls by exactly (d-1)V/A. The article carries the algebra the fifty-second version had no room for, plus the force balance on the sunk rock that shows the floor is where the argument closes.
At 3:15 the minute hand is on the 3 and the angle between the hands looks like zero. It is 7.5 degrees, or pi/24 radians, because the hour hand crawls a quarter of the way from the 3 to the 4 while the minute hand travels a full lap. The zero answer is exact for a clock whose hour hand waits on each numeral and jumps, which is not a clock that exists.
Strip the outer shell off a ten-by-ten-by-ten block of unit cubes and count what falls. The reflex answer, 271, is arithmetic done correctly on the wrong picture: a shell leaves from both opposing faces, so every axis loses two units and not one. Two independent counts land on 488, and the general shell turns out to grow like a surface rather than a volume.