Answer:
Pete -> Dan -> Ed -> Leo -> Ilya
Step-by-step explanation:
Quite tricky, but here it is.
If Pete stood in the middle, let's call it position 3.
He would be between Dan and Leo. Let's say Dan is at position 2, and Leo is at position 4. I got that from arithmetic, numbers before and after 3. In this scenario, we don't know we're both Ed and Ilya are.
Now, another says if Pete were to stand at the end, say position 5, he would be next to Ilya, say position 4. In this scenario, we don't know where Ed, Leo and Dan are, but we know for certainty they are ahead of Ilya since Ilya is 4th.
Last scenario, if Pete is standing in front of his friends, then who is where?
From the first scenario, we know that Dan is second, ahead of Leo.
From the second, we know that Ilya is just behind, so, Dan and Leo are ahead of him, yeah? That means we've established them in this order.
Dan -> Leo -> Ilya
And that leaves us with where Ed is.....
Going by the second scenario, we can adjudge that Ilya is the last person and thus, Ed is before him. If Pete stands in front with Dan at second, Leo at fourth and Ilya at fifth, that leaves us with the 3rd position for Ed.
So, we have
Pete -> Dan -> Ed -> Leo -> Ilya
