How Many Combinations Are Possible Using 6 LEGO Bricks?


Mathematician Søren Eilers was intrigued by a LEGO-related math problem. Let’s say you have six “standard LEGO bricks” (the rectangular 4×2 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… More at mental_floss.

An amazing number.

Categories: Misc

2 replies

  1. Well… Lego is amazing! Surely one of the best “inventions” 🙂

  2. How many of those are physically distinct? There must be an amazing number of duplication.

    Bricks 1, 2 & 3 are identical. Therefore the formation of 1 on 2 on 3, 2 on 3 on 1, 3 on 2 on 1, 1 on 3 on 2 and similar permutations would have the same physical character.

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