A puzzle was asked in a [mental ability test](http://hiqora.com/round-1/).

> 
> Arstil and Byzinte are two neighbouring islands in a far-off corner of the world. The natives of Arstil (the Arstillians) and the natives of Byzinte (the Byzintians) sometimes visit each other's sland. The 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 he didn't know which one. He 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 smart explorer then knew which island he was on.
> 
> 
> 

The question: **Which island is it?**

---

> 
> Another visitor came to one of the two islands. She met two islanders names Abs and Bags. She asked about them. They made the following statements:
> 
> 
> 

1. Abs: At least one of us is Arstilian.
2. Bags: Abs is Byzintian.

The questions are:

* **On which island did she, the wanderer, land?**
* **What about the nativity of Abs and Bags?**