Six standard 2x4 LEGO bricks can be combined in exactly 915,103,765 different ways.

The calculation of LEGO combinations is a complex problem in combinatorics. For decades, the LEGO Group cited a figure of 102,981,500 combinations for six 2x4 bricks. This number originated from a 1974 study by Jørgen Bak Bak, who calculated the possibilities for a tower of six bricks. However, his calculation was limited because it did not account for more complex, non-tower structures.In 2004, Søren Eilers, a professor of mathematics at the University of Copenhagen, decided to verify the figure using modern computing power. He discovered that the original 1974 calculation only considered bricks stacked in a specific vertical orientation. By expanding the parameters to include all possible three-dimensional connections, Eilers and his team found the true number to be 915,103,765.The team utilized a custom-written algorithm that ran for approximately one week on a high-performance computer to exhaust all possibilities. The math accounts for the fact that each 2x4 brick has eight studs, allowing for numerous offset positions and rotations. This exponential growth in complexity is why adding just one more brick to the set would increase the total combinations into the billions.