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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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Airbnb is Giving Away a One-Night Stay in Denmark's LEGO House
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The LEGO toy company opened its 130,000-square-foot LEGO house in Billund, Denmark, at the end of September. The attraction, which contains 25 million interlocking bricks used to make everything from furniture to dinosaurs, is a LEGO-lover’s fantasy. Now fans of the toy brand can enter for a chance to spend the night there.

For one night only, one lucky family will be invited to stay at the LEGO house after hours as part of a collaboration with Airbnb. The vacation begins with superstar LEGO set designer Jamie Berard greeting the guests upon arrival. Later, the family heads to the dining room to construct their food orders out of LEGO bricks. After the plastic requests are sent to the kitchen, edible versions of the meals are served by robot waiters.

The rest of the day consists of exploring the house’s galleries and experience zones. Guests can appreciate life-sized LEGO sculptures, browse iconic sets, or assemble their own one-of-a-kind creations. But the highlight of the trip has to be the suite where the family spends the night. The armchairs, books, alarm clocks, television, and pet cat are all constructed out of LEGO bricks. One of the only features that isn’t made of blocky plastic is the bed, which is nestled in a pool of bricks beneath a rainbow LEGO waterfall.

Living room made out of LEGO bricks.
Airbnb

“This really is a dream come true for any family with a passion for LEGO,” James McClure, Airbnb’s General Manager for Northern Europe, said in a statement. “I doubt there will be much sleeping as there is so much to enjoy in this incredible space.”

To enter, candidates must answer the question, “If you and your family had an infinite supply of LEGO bricks, what would you build?” in 50 to 550 characters. Submissions are open through November 16 and the winner and up to three guests will be flown to Denmark to commence their stay on November 24. The chosen visitors should be prepared to follow the house rules: LEGO-proof slippers are recommended, play is mandatory, and diving in the LEGO pool in search of that “one rare brick” is forbidden.

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New LEGO Set Honors NASA’s Female Pioneers
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For all their exemplary qualities, the LEGOs of yesteryear did have one flaw: the minifigures were predominantly male. In recent years, however, there’s been a notable uptick in female-focused sets, thanks in large part to fan-created concepts promoted through LEGO Ideas. One such project is the Women of NASA, a LEGO set celebrating some of the space agency’s most notable female figures that was posted to the LEGO Ideas last summer and has just been released for sale by the brick toy company.

The four notable NASA pioneers honored in the set are: computer scientist Margaret Hamilton, who played a major role in coding the flight software for the Apollo missions; famed first woman in space, Sally Ride; the "Mother of Hubble" Nancy Grace Roman; and astronaut and physician Mae Jemison, the first African American woman in space. (The original proposal also included Katherine Johnson, the mathematician at the center of Hidden Figures, but the company was reportedly not able to secure the needed approvals to feature her in the final set.)

The minifigures were created with set pieces like Hamilton’s stacks of code, scientific instruments, a microscale Hubble Space Telescope, a space shuttle, and more. The long-awaited 231-piece set officially went on sale on November 1; you can purchase it on Amazon for $24.99.


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