Professor Snape required four Gryffindor students (Bartholomew, Cassius, Delia, and Fred) to stay after class for (alleged) misbehavior. For their punishment, he told them to assist him in four different potions he needed made. He set them up in a small classroom - putting them at four desks arranged in a square, one in each corner (see diagram below).

The four potions Snape needed made were an Invisibility Potion, a Sleeping Potion, an Anti-Petrification Potion, and Wolfsbane Potion - every student was required to work on one of these potions. Each one of the potions required a different primary ingredient (Scales of Ashwinder, Venom of Doxy, Spine of Murtlap, and Toejam of Troll - in one order or another).

Can you figure out which student is sitting at which desk, which potion is being made by each student, and which ingredient corresponds to which potion?

1. Delia's desk is in the opposite corner of the room from the student making the Anti-Petrification Potion.
   
   
2. The desk of the student slicing the Ashwinder scales and the desk of the student making the Sleeping Potion are side-by-side.
   
   
3. When all four of the students were seated at their desks, the student making the Wolfsbane Potion is staring at the back of the student extracting the Spine of a Murtlap.
   
   
4. The student at desk 3 on the map (who isn't Cassius) is not the one making the Invisibility Potion.
   
   
5. The four students are: Bartholomew, the one making the Sleeping Potion, the one pouring the Doxy Venom, and the one using the Murtlap Spine.

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Solution:

The four students are Bartholomew, the one making the Sleeping Potion, the one pouring the Doxy Venom, and the one using the Murtlap Spine (clue 5). The student using Scales of Ashwinder can't also be using Doxy Venom or Murtlap Spine. The student using Ashwinder Scales is thus either Bartholomew or the one making the Sleeping Potion. But since the student using Ashwinder Scales is next to the one making the Sleeping Potion (clue 2), Bartholomew must be the one using Ashwinder Scales.

Since Bartholomew is the one using Ashwinder Scales, and the student making the Sleeping Potion cannot be using Doxy Venom or the Murtlap Spine, the student making the Sleeping Potion has to be using the Troll Toejam.

Now since the student using the Ashwinder Scales and the student making the Sleeping Potion are side-by-side (clue 2), and the student making the Sleeping Potion is using the Troll Toejam, that means that the students using Ashwinder Scales and Troll Toejam are one side-by-side pair and the students using the Doxy Venom and the Murtlap Spine are the other side-by-side pair.

Since the student making the Wolfsbane Potion is staring at the back of the student extracting the spines of a Murtlap (clue 3), that means that the Doxy Venom / Murtlap Spine pair are in Desks 3 and 4, in some order - meaning that the Ashwinder Scales / Troll Toejam pair are in Desks 1 and 2, in some order.

The student making the Wolfsbane Potion is in Desks 1 or 2 (clue 3) and is thus one of the Ashwinder Scales / Troll Toejam pair. Since the Troll Toejam is being used to make the Sleeping Potion, the Ashwinder Scales must be being used to make the Wolfsbane Potion (and we've already figured out that the student doing this is Bartholomew).

From clue 1, we know that Delia and the student making the Anti-Petrification Potion are in opposite corners, so one of them must be seated at either Desk 1 or Desk 2. We know that Desks 1 and 2, in some order, have the students making the Sleeping Potion and the Wolfsbane Potion, so neither one can have the student making the Anti-Petrification Potion. Thus, Delia has to be in either Desk 1 or Desk 2 - and since we know Bartholomew is using the Ashwinder Scales to make the Wolfsbane Potion, Delia must be the one using the Troll Toejam to make the Sleeping Potion.

The student in front of Bartholomew must also be the student in the opposite corner from Delia. Bartholomew (making the Wolfsbane Potion) is behind the student using the Murtlap Spines (clue 3), and Delia is in the opposite corner from the student making the Anti-Petrification potion - so the student making the Anti-Petrification Potion must be using the Murtlap Spines, and be in front of Bartholomew.

All potions and materials have been accounted for except for the Invisibility Potion and the Doxy Venom - the student using those must be seated in front of Delia, and beside the student using Murtlap Spines to make the Anti-Petrification Potion.

The person making the Invisibility Potion isn't at Desk 3 (clue 4), so student at Desk 4 must be the one making the Invisibility Potion, putting the student making the Anti-Petrification Potion at Desk 3, Delia at Desk 2, and Bartholomew at Desk 1.

Finally, the student at Desk 3 is not Cassius, so Cassius must be at Desk 4 and Fred at Desk 3.

To sum up:

	Desk One Bartholomew using Ashwinder Scales to make Wolfsbane Potion	Desk Two Delia using Troll Toejam to make a Sleeping Potion
	Desk Three Fred using Murtlap Spines to make an Anti-Petrification Potion	Desk Four Cassius using Doxy Venom to make an Invisibility Potion