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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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2000-Piece Fishing Store Set From LEGO Ideas Is Now Available to Buy
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LEGO

Not every concept that fans submit to LEGO Ideas makes it to the production line. Many designs don’t receive the 10,000 online votes required to move on to the review stage, and even when they do, that’s no guarantee they won’t be shot down by LEGO bigwigs. But the Old Fishing Store, one of the most ambitious sets that’s appeared on the site, is now available for builders to purchase.

Designed by Dutch LEGO fan Robert Bontenbal, the seaside building consists of about 2000 pieces, making it the largest LEGO Ideas set to date. It includes four human minifigures as well as animals like seagulls and a cat hanging around the bait shop.

Bontenbal, who works as an architectural draftsman, originally designed the set for his own enjoyment. “I liked it myself, and it looked so good so I decided to submit it to LEGO Ideas to see how the rest of the LEGO community liked it," he said in an interview with LEGO Ideas.

When he uploaded the fishing store set in December 2015, it took just six weeks to attract the 10,000 supporters needed to advance. Customers can purchase the real thing today through the LEGO shop for $150.

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Stop-Motion Artists Make LEGOs for Breakfast
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BrickBrosProductions, YouTube

LEGO bricks are made from plastic, but a clever stop-motion video makes the toys look tasty enough to eat. The filmmakers behind BrickBrosProductions—a LEGO-focused YouTube channel featuring stop-motion animations, tutorials, reviews, and more—created the film below, which follows a chef as he whips up a home-cooked breakfast using unorthodox ingredients: LEGO pieces crafted to look like butter, eggs, milk, bread, and jam.

The video took three days to film and was shot at a rate of 15 frames per second, Matthew—one half of the filmmaking team—told Ireland's The Independent. “The total amount of pictures taken for the brick film was 1500," he added.

Video edits took around two days to complete, and the filmmakers also added sound effects, including the real sounds of breaking eggs and pouring eggs. Hungry LEGO fans can watch the final product below:

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