A/N: Inspired by my own deadlines and a recent interest in Arithmancy, here is a quick oneshot (that might become more, complete for now) strictly Dramione friendship. Let me know what you think, this is my first time writing Potter despite being a fan for 14 years!

At this hour, the mermaids were most active, their songs an eerie yet pleasant echo in the Slytherin Common Room. Draco knew it was just past 3 in the morning – he rarely went to bed before 4am. The fire was burning low, a steady crackle that contrasted with the dull roaring of the Great Lake against the dungeon wall.

Draco sighed, rubbed his eyes and frowned at the essay he was working on. It was due in a few hours and he was completely stumped. Looking around the Common Room, he saw only a brooding fifth-year burrowed in a book, and a first year curled up in an armchair, fast asleep. Considering he was working on an Advanced Arithmancy essay, Draco didn't expect either to be of much use. Another deep sigh and Draco made up his mind. He grabbed a spare piece of parchment and scribbled a hasty note, hoping that it would find the recipient as awake as he was.

xxxxxxx

Hermione sniffed, her eyes burning from being awake for more than 36 hours. She cast one last glance at her finished essay and decided that she would warm her hands by the fire before turning in for the night. She revelled in the silence Gryffindor tower offered – since Harry and Ron were busy at the Ministry, she strangely missed fixing their homework, yet found it refreshing to be able to focus solely on her own studies. A sudden scurrying sound near the window drew her attention. Intrigued, she saw paper dragon, about the size of her fist, tapping against the glass. She let it in, and it looked at her expectantly. As soon as she touched it, the note unfolded in her hand, revealing a note from Draco Malfoy.

Granger,

My equation for the last question makes no sense. I completely understand that a + b is to a as a is to b, but I have no idea where to find the Golden Ratio in nature. I'm thinking pinecones, but that seems too simple and the equation makes no sense to me. Would you be willing to help?

D.M

Hermione chuckled. After returning to Hogwarts to complete her seventh year, she was somewhat surprised to see Malfoy back as well. They were the only two students studying Advanced Arithmancy with Professor Vector and their marks were almost identical. They were friendly, friendlier than before the war. Without Harry and Ron around to badmouth the Slytherin, Hermione learned that he wasn't all bad. Glancing at her watch, she sighed and sat down to write a note back.

xxxxx

Draco smirked as the note from Hermione arrived. He should have known that it would be a cat. He unfolded it, grateful that she was still awake to reply.

Malfoy,

I won't do your homework for you, but I will give you a clue. 8:5 is equal to 1.6, which is quite close to the Golden Ratio of 1.618. You're on the right track. See you in class.

H.G

With an exasperated groan, Draco slammed his head onto the desk, earning him a nasty look from the fifth-year who jumped at the sound. Draco sneered and went back to his essay. At least now he knew what to do. The second week of class loomed before him and he was probably going to enter it with no sleep.

xxxxx

The next morning, both Draco and Hermione were tired but relieved to hand in their essays to Professor Vector, who seemed quite jolly.

"Granger, Malfoy, I'm so glad you both stayed on for this class," she beamed. "You know, this is the biggest class I've ever had for Advanced Arithmancy. I'm looking forward to you both receiving an O on your NEWTS."

Hermione smiled and Draco even managed a half-grin. Perhaps this year wouldn't be so bad after all.