After the 6th episode, the SOS (namely Haruhi and Kyon) go and investigate the murder of Keiichi-san in his room. At first, they believe that Yutaka-san killed Keiichi-san after an argument and fled. However, after a search in the rain where Kyon saves Haruhi's life, Haruhi suddenly realizes that it wasn't what they thought it was. Back inside, Itsuki provides Kyon with more information about the murder. But in the end, it is all a hoax as Keiichi-san is not dead at all and Haruhi recounts the whole mystery with Kyon grumbling along. The next day, they leave the island and Itsuki reveals to Kyon that the people on the island were all espers working with him and the island was only created to the expense from preventing Haruhi's boredom.
Did You Know?
When Haruhi is explaining how she determined that the murder was a fake, she points her finger in an accusing manner exactly as Phoenix Wright does, who is the title in a series of video games in which players solve crimes in a detective-like fashion in a court room. After Haruhi is shown point her finger, Itsuki is show making a shrugging gesture identical to Phoenix's rival Miles Edgeworth. See more