Today’s question comes from the very talented maker of the Simon's Cat videos. Simon Tofield’s popular animations currently have over ten million views on Youtube. With the prevalence and ease of today’s computer animation tools, it’s rare to find high-quality, hand-drawn animation, particularly if you’re looking for something as funny and true-to-life as the Simon’s Cat videos. Hand-drawn animation takes a lot of work and a lot of pencils. How many times could Simon Tofield draw Simon's Cat using a typical HB pencil before the pencil ran out?
To solve this problem, we need to know two things: (1) how much graphite is in a typical HB pencil and (2) how much graphite is used on a typical drawing of Simon’s Cat1. An HB pencil is the same as the #2 pencil used for standardized tests, and these are about 18 cm (~7 in) long. A Simon’s Cat drawing2 will use different amounts of graphite depending on how big it’s drawn. I’ll assume the original sketch is as large as the picture of the cat as viewed on my laptop when I watch the video in full screen. If that’s the case, then the lines that make up Simon’s Cat should be about 10 cm (~4.0 in) if you stretched them out.
Now comes the difficult part. How much graphite gets used in a 13 cm long line? To get a rough idea, I took the #2 pencil on my desk and went back and forth with it 100 times on a piece of scrap paper 12 cm long. This is equivalent to drawing a 1200 cm long line. When I started there was about 3.0 mm of graphite showing and when I finished, there was 2.0 mm showing. From this, we can compute the amount of graphite used per cm drawn,
graphite used per cm drawn = (1.0 mm graphite) / (1200 cm drawn)
= 0.00083 mm of graphite used per cm drawn.
Using this, we can estimate how many Simon’s Cat drawings can be made out of a typical HB pencil,
# of cats = (graphite per pencil) / [ (cm per Cat) · (graphite used per cm) ]
= (18 cm) / [ (10 cm per Cat) · (0.00083 mm of graphite used per cm) ]
= 2200 Simon’s Cats.
Simon can draw roughly 2000 Simon’s Cats with a single pencil. This is a little larger than the number of frames in a one-minute movie.
Thank you, Simon. I like your cat.
 In How Many Licks?, I did a similar problem calculating how long of a line you could draw with a pen. I’m assuming we're talking about just the cat and not all of the background drawings.