Arstil and Byzinte are two neighboring islands in a far-off corner of the world. The natives of Arstil (the Arstilians) and the natives of Byzinte (the Byzintians) sometimes visit each other's island. Their strange thing is that whenever the islanders are on their home island, they tell the truth, but whenever they are on the other island, they lie.
One day an explorer landed on one of the islands, but didn't know which one. She then met two islanders, but didn't know whether they were from the same island or not. One of them said: "We are from different islands". Then the explorer asked: What island are we now on?" The other replied: "Arstil". The explorer then knew which island she was on. Which island was it?