“The LEGO Counting Problem”, Søren Eilers2016-05 (math)⁠:

We detail the history of the problem of deciding how many ways one may combine n 2 × 4 LEGO bricks, and explain what is known—and not known—about the related question of how these numbers grow with n.

…For decades, the LEGO Company (since 2005: The LEGO Group) would state in promotional material that 6 of the company’s iconic 2 × 4 bricks could be combined in 102,981,500 ways if they had the same color. The author coincidentally became aware that this number was incorrect in 2003, and in 2004 computed the correct number which is almost 9× larger. [915,103,765]

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Søren Eilers obtained his Ph.D. from the University of Copenhagen in 1995. He is currently on sabbatical from his position there, acting as the main organizer of the program “Classification of operator algebras: Complexity, rigidity, and dynamics” at Institut Mittag-Leffler in Stockholm. After being featured as the crazy mathematician in A LEGO Brickumentary, his Bacon-Erdős number dropped ∞ → 7.