A russian girl (Natalja Nikolajewna Djomkina, also known as Natasha Demkina) seems to be clairvoyant, she claims that she can see into the human body and can diagnose bodily illnesses. An american sceptics organization (Committee for Skeptical Inquiry (CSI) (at the time of the test calling itself CSICOP)) tests her. Seven people she does not know are shown to her, they wear sunglasses and show no obvious outer signs of their medical problems, body modifications or past surgeries that are their test attributes. One has an artificial hip joint, one had his appendix removed surgically, a third one has no diagnosis at all, etc etc. Natalia is given seven slips of paper, one after the other, each showing one body modification, symptom or surgery. She has to write the number of the person she thinks is the right one on the slip, and has to give it back before receiving the next one. Lots of representatives of the sceptics organization are present at the test, after which Natalja has 4 out of 7 right.
At first sight, intuitively, this seems only slightly over average random guessing (well, one more than half... shouldn't be too hard to archieve, bit of luck involved...).
But mathematically it is much harder, because if you guess one wrong, you automatically have another one wrong also.

This JavaScript program calculates the probability of having 4 or more out of 7 right when randomly guessing.

The TV report I have extracted the used data and test conditions from can be found here: "Das Mädchen mit den Röntgenaugen" on YouTube (unfortunately only in german language)

There is several reasons the Test was very hard for Natalja. None of the people used in the test actually asked for or needed help with a health problem from her. But that is what she usually did and was used to. Plus none of the people designing and executing the test had an interest in a positive outcome since they belonged to a declared sceptics organization. To the contrary: They had a strong interest in a negative result. Natalja was told that she would have passed the test if she had archieved one more correct answer. But, well, unfortunately... not enough. In reality, she archieved something that she had less than a one-out-of-fifty-chance to do without her abilities. No one told her she actually did amazingly well, and the probability also isn't mentioned in the TV report.

(Note: In the YouTube footage there is one contradiction: It is said that Natalja chose the person with the appendix surgery when asked for the person with the metal board in the brain, but deducing logically from the other given information, she must actually have chosen the person really having the esophagus issue. Also, the order of 4th and 5th question is not given. Both of these issues have no impact upon the outcome of the test or this simulation, since the number of right answers is clearly given.)