Pen is one of the six Pets introduced in the Even Care. She aspires to be a mathematician and is found in a room with an oversized piano on the floor and an octave counter despite the fact that she is completely deaf. She doesn't seem to have any clear relationships to any of the other Pets or characters.
In order to catch her, the player must solve a puzzle revolving around musical intervals. When the player steps on the piano, 2 clones are created at an octave apart (i.e from C to C on the piano, D to D, etc). Using a treadmill, the player can change a numerical counter that determines the location of Pen, starting from the far end of the piano. The correct solution is 7, as each musical octave on a piano consists of seven white keys (C → D E F G A B C).
Pen is an aspiring mathematician.
She's entirely deaf. She doesn't even know what sound is, let alone music.
I don't know what she's doing here.
Pen appears to be a somewhat humanoid entity- the most humanoid out of all of the pets, other than the three Care Pets. She wears a content expression upon her face, made up of two shut eyes, a perky nose, and a pursed mouth along with slight, pink, blushing cheeks. Her skin is a sour ochre color and she wears what seems to be a striped, brown beanie or yarmulke atop her large, round head. Draped on her pear-shaped torso is what seems to be a shawl or poncho of a dull terracotta color.
She hovers above the ground with what could be a black thread or thin appendage attached to her abdomen, with which her two outstretched hands are suspended. Pen seems to have six fingers on each of her hands and holds what looks like a snowball in her right hand, giving her the overall likeness of a scale as her hands teeter side to side with its weight.
Pen may be modeled after a tuning fork. This is supported by the fact that she is found in a room with a massive piano and is unable to hear or comprehend music, and that many of the rooms, including Michael's room, in the Child Gallery have what could be interpreted as a tuning fork (or tweezers) on their table.
The statement "I don't know what she's doing here," in Pen's description most likely refers to the fact that she is found in a room that houses a piano/revolves around music and that a deaf character would not normally be found in such a room or attributed to music.
Pen's outlandish holding of a snowball may be due to the fact that ballpoint pens can only function due to the ball itself, and ballpoint pens could be seen as a direct reference to Pen's name.