I am going to put an end to this thread.
This is the riddle: "An airplane is sitting on an enormous treadmill. As the plane starts its engines, the treadmill runs in the opposite direction at the same speed the plane is moving. Can the plane take off?"
The critical part is where it says, "the treadmill runs in the opposite direction at the same speed the plane is moving."
IMPORTANT
To answer the riddle, we have to know exactly how the "speed the plane is moving" is defined. Is it defined as the airplane's speed relative to the ground (surface of the treadmill) or its speed relative to the air around it? We do not know. The riddle is ambiguous. Therefore, there are two possible answers.
For simplicity, we will assume that the plane's take off takeoff speed is 150 mph
Let us consider the first situation, in which the airplane's speed is defined as speed relative to the ground (surface of the treadmill).
The plane accelerates to 150 mph relative to THE SURFACE OF THE TREADMILL. The treadmill, in accordance with the riddle, moves backwards at 150 mph. If the treadmill is moving at negative 150 mph, and the plane is moving at positive 150 mph RELATIVE TO THE TREADMILL, then the plane is not actually moving forward relative to the air around it. There is no air flowing over the wings. The wings do not generate lift. The plane does not fly.
Let us now consider the second interpretation of the riddle, in which the plane's speed is defined as speed relative the the air around it.
The plane accelerates to 150 mph relative to the air around it (airspeed). The treadmill goes backwards at 150 mph, but it doesn't matter. The wheels are spinning at 300 mph, and the plane's engines have to work roughly twice as hard as they normally would to get up to 150 mph (the plane's entire weight is resting on a surface that is moving backwards at 150 mph), but the plane is still moving forward at 150 mph relative to the air around it. The air is flowing over the wings at 150 mph, and the wings generate enough lift for the plane to take off. The plane flies.
There is not a right or wrong answer to the riddle. There are two different interpretations, because the riddle is ambiguously worded. The two interpretations lead to two different answers.
End of argument.