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How Many Combinations Are Possible Using 6 LEGO Bricks?

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Mathematician Søren Eilers was intrigued by a LEGO-related math problem. Let's say you have six "standard LEGO bricks" (the rectangular 4x2 bricks seen in the original LEGO patent). If you fit them together, how many possible structures can you make?

This question was first officially "answered" in 1974, and LEGO mathematicians arrived at the number 102,981,500. Eilers was curious about the mathematical methodology behind that number, and soon discovered that it only covered one kind of stacking—thus, it was dramatically low. So he wrote a computer program that modeled all the possible brick combinations. After running the program for a week, he ended up with a massive number: 915,103,765 combinations.

(Incidentally, Eilers encouraged high school student Mikkel Abrahamsen to write another program in a different programming language, on a different computing platform, without consulting on the solution or methodology. When Abrahamsen's program concluded, the math matched up—and Abrahamsen's method for computing it was actually superior!)

Then, of course, Eilers had to ask what happened if you added a seventh brick, or an eighth, and so on. The math gets exponentially more time-consuming with each addition. Even with a revised version of his program running on a modern computer (which can now handle the original six-block calculation in just five minutes), calculating the eight-brick solution takes about three weeks, and a nine- or ten-brick solution would "probably take years. Maybe hundreds of years."

Here's a brief clip from the documentary A LEGO Brickumentary in which Eilers explains how it all came together:

Of course, because Eilers is a math professor, he put all the math online for fellow nerds to peruse. There's a lot on that page to digest. I enjoyed this snippet from the page in which he considers the possibility of a 25-brick solution (emphasis added):

With the current efficiency of our computer programs we further estimate that it would take us something like

130,881,177,000,000,000,000,000,000,000,000,000,000,000

years to compute the correct number. After some 5,000,000,000 years we will have to move our computer out of the Solar system, as the Sun is expected to become a red giant at about that time.

If you like this stuff (and have the math skills to decipher it), dig into the academic paper "On the entropy of LEGO" by Bergfinnur Durhuus and Søren Eilers.

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The 5 Biggest LEGO Sets Ever Made
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While technology focuses on making everything smaller, Denmark-born company LEGO has seen unprecedented success making everything bigger. Their official build kits can number in the thousands of pieces, enough to construct elaborate, towering, and massive objects. If you have a lot of spare time and patience, take a look at the five biggest LEGO sets ever made.

1. TAJ MAHAL

The LEGO Taj Mahal sits on display
Jose Sa, Flickr // CC BY 2.0

Originally released in 2008, LEGO’s Taj Mahal set wowed collectors and casuals alike with its devotion to detail. Consisting of 5922 pieces, it remains the largest set on a per-piece basis of any LEGO set ever made. (It also comes in at a towering 16 inches when completed.) In 2010, soccer star David Beckham told an interviewer that he spent much of his spare time in Italy between games building the set.

2. ULTIMATE COLLECTOR’S MILLENNIUM FALCON

The LEGO Millennium Falcon sits on display
Ronny Nussbaum, Flickr // CC BY-ND 2.0

It would be nearly 10 years before a new Star Wars film arrived in theaters, but in 2007 LEGO decided to release their most complex Force-related product yet: the 5197-piece Millennium Falcon. To help fans appreciate the scope of this build—which measures three feet by two feet when completed—Gizmodo’s unboxing video revealed that the instruction manual alone weighs four pounds. It’s currently regarded as the most valuable LEGO set ever released, with resales averaging nearly $4000.

3. GHOSTBUSTERS FIREHOUSE HEADQUARTERS

The LEGO Ghostbusters Firehouse entrance is shown
Vincent Teeuwen, Flickr // CC BY 2.0

The arrival of 2016’s Ghostbusters reboot brought with it a sea of merchandising. One of the few to cross the streams and feature characters from both the current version and the original 1984 film was the LEGO version of their firehouse office space, which clocks in at 4634 pieces. While the towering frame of the building requires plenty of bricks, it’s the detail inside that ups the part count: Opening the firehouse reveals tons of tiny details taken from the films, including a dancing toaster and the zombie cab driver.

4. TOWER BRIDGE

The LEGO Tower Bridge is one of the biggest LEGO sets ever made
Norbert Schnitzler, Flickr // CC BY-SA 2.0

A brick-perfect replica of London’s famed crossing over the River Thames, the Tower Bridge was released in 2010 and comes boxed with 4287 pieces. The set features a working drawbridge and more than 80 tiny windows.

5. BIG BEN

The LEGO Big Ben set appears on top of a map
Matt Brown, Flickr // CC BY 2.0

The latest in the biggest LEGO sets ever made, 2016’s Big Ben clocks in at 4163 pieces. The completed work stands nearly two feet tall. LEGO designers also went for some synergy, noting that the scale of Big Ben and the London Bridge are comparable, making them a perfect co-display—and a testament to your towering patience.

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LEGO Built a 9-Foot-Tall Statue of Liberty in the Smithsonian
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The Smithsonian's National Museum of American History has a new wing, and it's celebrating with a giant LEGO masterpiece. The just-opened second-floor renovation of the museum focuses on American democracy with exhibitions on the theme "The Nation We Build Together." As such, the museum teamed up with LEGO to honor that symbol of the American melting pot, the Statue of Liberty. LEGO designers created a 125-pound, 1:32 scale replica of the New York City statue for display at the museum, where it will remain until the end of the year. In total, it rises 300 LEGO bricks tall (9 feet) and contains 25,375 pieces. Led by LEGO Master Builder Erik Varszegi, it took four builders 292 hours to put it together. You can watch the process in LEGO’s timelapse below.

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