So, how would you move Mount Fuji?

That seems to be the question everyone is asking.  A couple of months ago I wrote a little review of "How Would You Move Mount Fuji", a book about technical interview questions written by William Poundstone.  In this review I "solved" several of the puzzles.  Subsequently I posted a discussion about The 21$ Question, and also Revisited the Bridge of the Programmers, then later did More Bridgework, and Even More Bridgework.  Not to mention solving The Two Switches.

So - I periodically monitor the searches people do which lead them to this site, and "Moving Mount Fuji" is one of the most popular.  It would seem that people are looking for the answer, rather than looking for a review of the book.  So I decided to answer the question!  This is one of those questions which doesn't have a "right" answer; basically the interviewer asks the question to see how you think.  Any semi-logical series of assumptions and deductions which leads to a reasonable answer would be good.  Failing to attack the problem at all or giving up would be bad.

In this, it resembles a question I quoted from the book in my review,How many piano tuners are there in the world?  (Here's the answer I gave for that one.)

Okay, we want to move Mount Fuji...  So we have to make some assumptions.  First, we have to define what "moving" means.  So let's say we are going to move the entire mountain to Mojave, California.  Hey, it's desert, there's a lot of room out there.

First let's consider the overall technique.  We need a bunch of dynamite to blow up the rock.  Then we need bulldozers to pick up the rock and put it into trucks.  We use the trucks to carry all the rock to the nearest airport, where we have a fleet of 747 cargo jets waiting (and loading equipment).  From there we fly the rock to Mojave, unload it from the planes, transfer it back into trucks, move it into the desert, and dump it.  And we'll need bulldozers to push the rock back into shape.

There is a philosophical question as to whether, having moved all the rock and reshaped it, we still have Mount Fuji.  We certainly have the parts to Mount Fuji, but is the mountain still the mountain after it has been moved in this way?  I'll leave the philosophy alone (for once!) and just say we stipulate up front that moving the parts is equivalent to moving the mountain.

Next we have to figure out how big the mountain is...  Well, I Googled and figured out it is 3,776 meters high (about 13,000 ft.).  I might have guessed about 12,000 ft. without Google because that's about the height of Mt. Whitney (the tallest peak in the California Sierra Nevada range).  The shape of this mountain is nearly a perfect cone, with the width of the base about three times the height.  As you know, the volume of a cone is given by:

(base area * height) / 3 = (πr² * height) / 3

So this means the volume of Mount Fuji is approximately:

(π * 18,000 * 18,000 * 12,000) / 3 ≈ 4 x 10¹² ft³       [ 1/8/14 - thanks for fixing my arithmetic, Jay ]

That's a lot of rock.  Next let's figure out how much this might weigh.  Imagine a rock the size of a cubic foot.  Could you pick it up?  I'd say barely.  It probably would weigh about 100 lbs.  So that means we have a lot of heavy rock to move:

4 x 10¹² x 100 lbs = 4 x 10¹⁴ lbs = 2 x 10⁹ tons

Cool.  Okay, so how many 747s would we need?  A 747 can carry about 500 people with all their luggage.  The people weigh about 150 lbs on average, and their luggage probably weighs about the same, so we're talking 500 x 300  = 150,000 lbs, or about 75 tons.  Let's say for cargo purposes we could carry 100 tons.  Would that be the limiting factor, or would volume?  Well, if each ton is about 20 cubic feet, then we're talking about 2,000 cubic feet.  That's 10 ft x 10 ft x 20 ft, so clearly the size of the rock would not matter.  (Actually since the rock would be broken up it would take more space, but not that much more.)  We would therefore need 2 x 10⁷ = 20M plane flights.  If we had a fleet of 1,000 planes flying in parallel, and each plane made two flights per day, it would take 10,000 days or around 33 years.

That's a long time, but this is a big project.  Many of the great European cathedrals took over 100 years to build, as did the Great Wall in China and the Great Pyramid in Egypt...

What about trucks?  Well, I'd guess a really big dump truck could haul 25 tons.  (That would be about 5,000 cubic feet, or 10 ft x 10 ft x 50 ft, roughly speaking.)  So we'd need four times as many trucks as planes.  I don't know how close the nearest airport is to Mount Fuji, but let's assume we could make two trips from the mountain to the airport each day (same as plane flights), so we'd need 4,000 trucks.  No problem.  Oh yeah and we'd need about the same number of trucks on the other end, too.

Now, about those bulldozers.  Well, let's say it takes one bulldozer to load one truck.  We assumed the trucks make two trips per day, so now let's assume a trip is really four hours of loading, four hours of driving, and four hours of unloading.  That would give a bulldozer four hours to do the loading, and that seems reasonable.  So pencil in 4,000 bulldozers.  I'm sure there would be some traffic problems with that many bulldozers roaming around the mountain, but we could deal with that.  No worse than the Ventura Freeway at rush hour :)  And as with the trucks we'd need the same number of bulldozers to rebuild the mountain in Mojave.

So, that's how I'd move Mount Fuji into the Mojave desert.  Give me 8,000 bulldozers, 8,000 dump trucks, 1,000 cargo jets, and (of course) the people to man them, and it would take me about 33 years.  No problem.