## Tuesday, June 1, 2010

### Special Guest: Maryellen Hooper

Today’s question comes from the very funny comedian Maryellen Hooper.  Ms. Hooper has appeared on The Tonight Show with Jay Leno and in her own Comedy Central special, Lounge Lizards.  In 1998, she was awarded “Female Comedian of the Year” at the American Comedy Awards.  She writes,

“I've decided to ask a question on behalf of my son, Nate and his best friend, Noah. They're 5 & 6 years old…How many Legos would it take to build a ladder to the Moon?”

I’ll assume we’re using the standard 8-peg Lego brick.   A single Lego is 9.6 mm tall, 32 mm long, and 16 mm wide1.  By multiplying these together, we can calculate the Lego brick’s volume to be about 4.9 cm3.  To find the total number of Legos needed, we have to estimate the dimensions of the ladder.

The Moon is about 380,000 km away from the Earth.  I’ll assume the sides and rungs of the ladder are both 6.0 cm wide and 6.0 cm thick.  I’ll also assume the rungs are 60 cm (~2.0 ft) long and that adjacent rungs are separated by 30 cm (~ 1.0 ft).  With this rung separation, there will be about 1.3×109 rungs.  From this we can compute the total volume of the ladder.

volume = (# of sides) · (volume of the sides) + (# of rungs) · (volume of the rungs)
= 2 · (6.0 cm · 6.0 cm · 380,000 km) + 1.3×109 · (6.0 cm · 6.0 cm · 60 cm)
= 5.5×109 m3.

To find the number of Legos we’d need to build the ladder, we just need to divide the volume of a single Lego into volume of the ladder,

# of Legos = (ladder volume) / (Lego volume)
= (5.5×109 m3) / (4.9 cm3 per Lego)
= 1.1×1015 Legos

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A Lego ladder to the moon would require 1.1 quadrillion Legos!2  Using prices from Lego’s website, this would cost about \$51 trillion dollars.  At his richest, Bill Gates was still 500 times too poor to afford this.  Thanks for the great question, Maryellen!

You can find Maryellen’s tour dates and clips of her doing standup on her website.  You can also buy her comedy CDs Fixer Upper and Dignity Under Duress.

[1] Apparently, the good people at Lego are too good for the metric system, so they actually made up a “Lego Unit”.  One Lego Unit is equal to 1.6 mm.
[2] Yes, “quadrillion” is a real number.

1. I don't think that 1.1 quadrillion Legos would do the job. For an upcoming question I suggest that you ask how tall a tower can you build of Lego on the surface of the Earth before the lower layers are plasticized from the vertical force from the weight of the tower.

2. I bow down to your awesomeness, Aaron Santos. Both Nate and Noah yelled, "NO WAY!" and high-fived each other. You are the King, my friend.
Maryellen

3. i believe you've failed to consider the forces that will be exerted against your lego tower... so yes, in an advertising for lego, and 3rd grade math sort of way... you are correct. in any other light you're painfully wrong and if anything suggesting falsehoods to your readership. you are dispersing LIES. you are a LIAR.

4. What about a lego stairway to heaven?

5. I think anyone that is complaining about the fact that she did not consider the compression forces of gravity is an idiot. Of course it's going to collapse under its own weight & of course you can't actually build a ladder to the moon. Thank you for pointing that out - without you we would all be blindly led astray and begin building our own Lego ladders to the moon. It pains me to read comments like that of Madd Scientist. You Sir, are an idiot. The Burj Kalifa is 870ish meters high and is near the limit of construction. Obviously its not built from Lego.
I think its a fun question and a fun answer. Thanks for figuring out an interesting question. Ignore those that want to point out the most obvious problems with your answer. Thanks