The number of ways to combine N bricks into a tower of We predict that it is impossible to find efficient formulae to compute Problem, and here is a good one to point out. Mathematics is a vivacious research area with lots of open Mathematics most people encounter during their education is Is somehow complete is probably induced by the fact that the Mathematicians often get the question of whether there is anything Problems which do have an impact on everyday life. Practical applications (like this one) are useful to study Happens that methods developed to study a problem with no Important to drive mathematical research, and it oftens Thus this is mainly interesting as a challenge for mathematicians: ToĬompute or at least estimate the number of ways to combineĪ given number of two-by-four LEGO bricks. Move our computer out of the Solar system, as the Sun is expected toĬlearly nobody really needs to know exactly how many ways there are to combineĦ or more LEGOs, as clearly demonstrated by the fact that LEGO hasĭone very nicely with the smaller number over several decades! After some 5,000,000,000 years we will have to We estimate the total number of ways to combine 25 two-by-four LEGO bricks to Thus one has toĮssentially go through all the possibilities. The mathematics of the total number of combinations is so irregular that it is veryĭifficult to come up with a formula for it. That this isĪ 40 digit number causes no problem, because we Ways to combine 25 two-by-four LEGO bricks into a tower of height 25. It is worthwile to point out that it is not the size of the number Obviously this has been forgotten over the years. He only intends to count the towers of maximal height. LEGO corporate newsletter Klodshans in May 1974 clearly states that Jørgen Kirk Kristiansen, who has carried out the At the time when the computation was done such computers
Seem to be impossible without access to a relatively powerfulĬomputer. Purpose of the calculation must have been to convince the public that It may seem surprising that LEGO has not found the larger number, since the Why didn't LEGO compute the correct number? The number of configurations of various heigts are
#What are the dimensions of a lego brick windows#
Is written in Pascal, executed on an Intel Machine with Windows XP and uses an iterative The program subsequently developed by Mikkel Abrahamsen The program first developedīy Søren Eilers is written in Java, executed on a G4 Apple Powerbook, and uses a recursive counting To avoid error, we have independently developed two different computer programs andĮxecuted them on different platforms. This is a computation which takes about half a week on We have written computer programs to systematically generate and countĪll the different configurations with six two-by-four studded How does one arrive at the number 915,103,765? Just because the calculator used at the time did not have the capacity for 9-digit numbers. Note that the number reported by LEGO is off by four. There are 2 5 symmetricĬonfigurations, but the remaining 46 5-2 5 configurations To build a tower with six bricks, one can choose among the 46 Rotating the lower brick 180 degrees so we see that the number ofĭifferent combinations of two LEGO bricks of the considered size is Of the other combinations have doubles which can be achieved by However, only the blue combinations here are unique. If oneįixes the position of the lower LEGO brick, the second can be put on top in
How does one arrive at the number 102,981,500?Ĭonsider first how many ways two two-by-four LEGO bricks can be combined. LEGO has counted allīut neglected all the lower configurations, like Indeed, it is a main feature of LEGO that one canĬombine the bricks much more freely. But when oneīuilds with LEGO one does not have to put each brick on top of the Height six with two-by-four studded LEGO bricks. This number is - roughly - the number of ways one can build a tower of LEGO LEGO is a registered trademark of the LEGO Company. The ultimate LEGO book (turn to page 9).Mikkel Abrahamsen on Danish national news (TV2 Nyhederne) in streamed video.How does one arrive at the number 915,103,765?.
Straightforward computer calculation we have found that the However, the number is wrong - very wrong. Consequently, the number can be found in severalįact" books and on more than 250 home pages in a multitude of languages. The ultimate LEGO book (Dorling Kindersley, 1999). This number was computed at LEGO in 1974 and hasīeen systematically repeated by LEGO Company since, for instance in Two-by-four studded lego bricks of the same color is A LEGO Counting problem It is commonly believed that the number of ways to combine six
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