Fermi Contest 3

Same rules as before.  The winner gets a signed copy of How Many Licks?  Email your entries to "aaron at aaronsantos period com" by May 1, 2010 to be eligible.

This is a problem that has vexed me for a while, but I think I finally have a good method to solve it: How far would the oceans sink if we took all the fish out?

Twitter

I’m told Twitter is a great way to get exposure.  Not including family and friends, I get a new follower about once every eight days.  To reach Sarah Killen’s follower status, it will take me 622 years. 

Follow me @aarontsantos.

We Have a Winner!

At long last, Mario finally gets some help.  We have a Fermi contest winner!

How many times has our lovable Italian, shall we say, left the platform?

According to Wikipedia, over 210 million Mario games have been sold, but this doesn’t include the number games that have been downloaded, purchased at yard sales, or resold on E-bay.  To account for these extra players, I’ll assume 400 million people have owned Mario games.  One usually gets bored with a game after a few months at which point the amount of game play decreases.  If you average an hour per day for the first few months, then you’ll have about 100 total hours of game play in this time.  Occasionally, nostalgia kicks in and you start playing again.  I’ll assume 100 hours of nostalgia play giving a total of 200 hours per player.   Some players are so good they never die, but most Mario players, or rather their Mario avatars, die fairly regularly especially when starting out.  A reasonable estimate is one Mario death per minute.  I say “reasonable” because even terrible players don’t die every 6 seconds, and even fairly good players usually can’t last 10 minutes without accidentally falling into a bottomless pit.  Using these numbers, we can estimate the total number of Mario deaths:

# of deaths = (# of game owners) · (hours of play per owner) · (deaths per minute)

= (400 million game owners) · (200 hours per owner) · (0.5 deaths per minute)

= 4.8×10¹² Mario deaths

Congratulations to our winner, Melgamoose!

A couple of observations about the contest

There really weren’t any bad entries.  There were 29 entries in total and the average answer was 8.35×10¹² Mario deaths.  This makes me feel reasonably confident that my answer isn’t too far off since it’s within a factor of 2 of the mean.  Fermi estimates are only expected to be good to within an order-of-magnitude, so it’s interesting to look at the distribution of magnitudes:

The mean magnitude was 11.5 and the standard deviation was about 1.3, i.e. roughly an order of magnitude.  This tells me two things.  First—forgive the sucking up—I have a really smart readership.  Second, just about any of these answers could reasonably have won the contest.  So please enter our next contest which will be announced this weekend, because next time the winner could be you!

A New Type of Carrier Pigeon

Long before we had cars we had horse drawn carriages.  Doesn’t this mean that we should also have had bird drawn planes?  How many pigeons would it take to carry a 747?

According to Wikipedia, the Boeing 747 has a maximum take-off weight of 442,000 kg (~975,000 lbs).  Since birds build nests, we know that a pigeon is strong enough to carry a twig.  Wood densities vary, but they’re roughly about 500 kg/m³. This means that a 5 mm thick 10 cm long twig would weigh about 1.3 g.  From this we can compute the number of pigeons needed to carry a 747.

# of birds = (mass to be carried) / (mass carried per bird)

= (442,000 kg) / (1.3 g per bird)

= 3.4×10⁸ birds

It would take about 340 million pigeons. This is much more than we could realistically harness to a plane, which is probably good given what pigeons typically do to your car.

Check in tomorrow to find out who won the Mario Estimation Contest.

Get your final answers in!!!

Only one more day to submit your answers to the Mario contest.  In all the video games ever played, how many times has Mario died?

Zit Vac

Whether it was the prom, a first date, or an important job interview, everyone’s had some special event ruined by a zit.  For times like these, it’d be great if there were a Hoover vacuum¹ attachment that could suck the pore open again.  Is this physically possible?  How much of a pressure difference would you need to vacuum off a zit?

Many zits can be popped with just your fingers, but we’re really interested in the diffcult-to-pop zits².  For that reason, we’ll consider zits that are at least as strong than as the maximum force our fingers can produce.  It’s difficult to know one’s finger strength a priori, but this site suggests that a healthy thumb should produce a maximum force of about 200 N while a healthy index finger may produce 100 N of force.  This force squeezes on the zit causing the internal pressure to increase and the skin to deform.  The deformation may absorb some of the force so that the pressure inside the zit is less than it would be otherwise.  For simplicity, I’m going to neglect this effect and assume the force gets applied directly to the zit over an area of about 0.25 cm².  From this, we can estimate the pressure needed to pop a zit.

pressure = (total force) / (area)

= (300 N) / (0.25 cm²)

= 1.2 ×10⁷ Pa.

That’s about 2000 psi³.  It’s also about 120 times larger than atmospheric pressure, meaning that even with a perfect vacuum there’s no way to build up enough of a pressure difference for this to work⁴.  This makes intuitive sense as anyone who’s tried to vacuum a zit off can tell you.

[1] I imagine it will look something like that tube at the dentist’s office that sucks up your face.

[2] Why use a Hoover attachment when you can just use your fingers?

[3] Good call, Boomer!

[4] Mr. Wizard did an experiment similar to this where they tried to see how far you could suck water up a straw.  I’ve been unable to find video of this online, but here’s one just for nostalgia’s sake.

Engaging Gauging

A friend suggested posting problems the day before the answers so that readers have a chance to solve them on their own.  I like that idea so I’m going to try it out today.  Feel free to post your solutions in the comment section.