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## How Many Ways Can You Combine Six Legos?

by | Jan 18, 2022

How many ways can you combine six LEGO bricks of the same size and color? Before knowing the answer I guessed a few thousand and thought I was probably overshooting. It turns out that I massively underestimated the answer.

In 1974, for whatever reason, LEGO computed the answer to this seemingly straightforward question and arrived at 102,981,500 combinations. Wow. That’s a lot of ways to combine six LEGO bricks!

But it turns out that number is wrong because LEGO didn’t use all the possible ways to combine the bricks. The correct number was calculated by mathematicians at the University of Copenhagen in 2005 and is 915,103,765!

To come up with the correct answer, the mathematicians had to write a program to solve the problem. In 2005, it took the computer a week of calculating to come up with the answer. Using a current computer would still take over five minutes. Interestingly, the answer was checked by a high school student who wrote his own program and came up with the exact same answer.

Here’s one of the diagrams from the paper calculating the correct number, which I found helpful in grasping how there can be so many combinations of LEGO bricks:

I think this fact — that there are nearly a trillion combinations of six LEGO bricks — sheds light on the world in which we live. There are way more combinations of factors that shape reality than we realize. If six LEGOs can generate such a huge distribution of results, think about the 3 billion base pairs in the human genome. It also reminds me of Littlewood’s Law of Miracles that states that on average we can each expect a “miracle” once a month. Here’s an IFOD about Littlewood’s Law.

Here’s a bonus fact about LEGOS: the company is the largest producer of tires in the world.

1. I thought I have an inquiring mind. Apparently, not so much…at least, not compared to people who ponder these kinds of problems, ha!

2. I do not doubt the number. Now, I wonder how many cells there are in the Omicron Virus that could mutate into a new variant?

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