Clone Thought Experiment: The Dilemma

This is supplementary material to the question posed in Clone Thought Experiment.

We'll presume our situation to be exactly the way it was in the previous thought experiment, except this time, as you and your clone are being lead into the room, you are instead seated next to each other.
Sitting on the other side of the table is a tall, thin, and serious looking man in his 50's.

He explains that overnight there was a power surge that deleted all of the facilities documentation and files.
Every security camera tape had been erased and in the darkness there was much confusion.

His point being, the facility has lost track of which room you were placed in and which room the clone was placed in.

How can you go about telling yourselves apart?

Clone Thought Experiment

PREFACE
For the sake of this thought experiment, we will use the marvels of Science Fiction to create a Clone that is an exact duplicate of you right now, with all your same features and memories.


One evening you enter a cloning facility.
Upon entering you are greeted by an orderly and escorted to a plain room with a single bed.
You lie down on the bed and fall asleep.
The following morning you are awoken by the same orderly and lead into a white room.
Centered in the white room is a square table with two chairs.
Each chair has in front of it one sheet of paper and one sharpened number two pencil.
Across the room you notice another orderly, looking exactly like your orderly, simultaneously guide your clone into the room and towards the table.
You and your clone are then seated at the table and left alone.
A disembodied voice instructs you and your clone to draw a picture.


Will you and your clone draw the same picture?