## Friday, April 23, 2010

### Simon Says

Author, journalist, and TV producer Simon Singh1 has a great question for us today.  Dr. Singh has written numerous popular science books including Fermat's Enigma, The Code Book, and Big Bang: The Origin of the Universe.  His question is this:

“How many razor strokes does the average clean-shaven grown up man make each morning?  People typically say 20 or 30, but when they count them they see that it is about ______.”

I’ve left Dr. Singh’s estimate blank.  Without counting, how many razor blade strokes does a man make each day?

How many strokes you use clearly depends on how much facial hair you have, your shaving technique, and what kind of razor you use.  You almost certainly make more strokes with a dull single blade then you will with a brand new 5-blade razor2.  It’s difficult to measure the area of ones face since it’s not a flat surface, but a reasonable estimate3 is 7 in. by 8 in = 56 in2.  Some times you use strokes that cover several inches, other times your razor moves only a few millimeters.  Let’s assume the average stroke covers one square inch of area.  If you’re like me, you usually like to shave each area a few—let’s say 3—times to make sure it’s smooth.  From this we can estimate the total number of strokes,

# strokes = (total area) · (strokes per unit area)
= (56 in2) · (3 strokes per in2)
= 170 strokes.

This is within an order of magnitude of Dr. Singh’s estimate of 100 strokes.  For the record, I just counted and got 257 strokes with a fairly dull Gillette Fusion.

Dr. Singh, thank you for both for the great question and for your heroic work fighting for free speech.

[1] For those of you who read this earlier and are wondering why the attribution changed, it's because I screwed up.  I had written Dr. Singh and he was kind enough to reply with the above question.  Somehow I mixed up his email address with Simon Tofield's who had submitted a question earlier.  I'd like to give my sincerest apologies to both Simons for my stupid and very embarrassing mix up.
[2] The Onion was fairly clairvoyant on this one.
[3] I actually measured this to be sure.  It may seem large, but I’ve got one of those necks where you can’t quite tell where the facial hair stops and the chest hair begins.