One summer day John was jogging in the countryside wearing only his normal running clothes (shorts, vest, sports shoes and socks). After running for some time he saw that the lace of one of sports shoes was untied. While he was bending down to tie it up, a psychopath who was hidden nearby, approached him from behind and hit him on the head so hard that John became unconscious.
When John recovered he found that he was inside a perfectly cylindrical room about 20 meters diameter and 5 meters high. The walls, floor and ceiling of the room were perfectly smooth and symmetrical and had no visible feature so it was impossible to distinguish any particular direction inside the room.
Inside the room there was a cage. The cage itself also was in the shape of a perfect cylinder about 2 meters diameter and 2 meters high.
The cage was made of solid steel and it had only a very small spherical light bulb inside fixed exactly at the centre of the roof of the cage, and a solid door on one side. The light bulb was fixed to the roof, so that it rotated together with the cage. It was not possible to see anything outside the cage when someone was inside the cage and the door was closed (nor was it possible for someone outside the cage see inside after the door was closed)
The cage was placed on a perfectly circular platform exactly the same diameter as the cage. The platform can rotate clockwise or anti-clockwise at the discretion of the psychopath, who uses a remote control to start and stop the rotation. The platform starts and stops rotating at a very slow rate of angular acceleration, so slow that someone inside the cage cannot even feel when the platform starts to rotate and when it stops. Also the maximum speed of rotation is so slow that a person inside the cage cannot feel any centrifugal force so he doesn’t even have any idea about how fast the cage is rotating.
The psychopath then told John that he will challenge him to do a task. If he fails he will die, as have many others before. However, if he succeeds his psychopathic ego will be destroyed, John will be released and the psychopath will give himself up to the police.
The task consists of this. Surrounding the cage on the floor of the room about 10 meters from the center of the cylinder there are eight glasses each filled to the top with an orange liquid. The glasses are placed at the eight cardinal points: North, Northeast, East, Southeast, South, Southwest, West and Northwest. One of the glasses is filled up with pure orange juice. The other seven glasses have orange juice with a small amount of deadly poison mixed with the juice. It is not possible to distinguish between the glasses or their contents in any way at all except by tasting the liquid. John is not allowed to go anywhere near the glasses to examine them before the test starts.
The psychopath then tells John that the only glass without poison is the glass placed in the north direction and tells him which one it is.
The psychopath does not allow John to leave any mark or object on the floor of the room by which to indicate a particular direction.
Then the psychopath tells John to get into the cage and the psychopath closes and locks the door. The psychopath remotely turns on the little light in the cage and gives John a couple of minutes to get used to the environment inside the cage. The psychopath then slowly starts to rotate the cage for about one minute then slowly stops the rotation (which takes about another minute). The psychopath waits another couple of minutes then unlocks the door and tells John to get out and choose a glass from among the eight and to drink it all.
Before the psychopath unlocked the cage door he had already changed his own position in the room to make sure John was totally disoriented when he got out of the cage and had no possible way to tell from his surroundings in the room which direction he was facing.
John got out of the cage, quickly chose a glass of juice and drank it. The psychopath was amazed to see that John did not immediately fall down dead so he knew that John had chosen the right glass. He then told John to repeat task many more times until he realized that John had not chosen the right glass the first time just by luck.
John was released and the psychopath was put in prison for rest of his life.
How did John manage to succeed in doing the task?
NOTE: Everything that is described could actually have happened in real life on this Earth.