Lego Superheroes and Combinatorics

My son (age 5) has developed the most fascinating (for both of us) new hobby of creating his own Lego superheroes by rearranging the ones that he has. He’s spent hours on this recently, meticulously dismantling them and looking for exactly the right piece to create the character he wants. Behold, a few recent versions:

He refused to tell me their names and got shy when I asked, but from what I can put together it’s (from right to left): Joker in disguise, Queen Tut/Barbara Gordon, Robin ripping his pants off, Happy Bug Man, Caveman Scarecrow and Spidergirl.

Never one to let a good analogy go, I attempted to explain to him that he’s figuring out how many combinations there are for any group of Legos. For example, if we wanted to know how many unique creations we could make out of the pieces in the picture above, we could make over 70,000 unique characters. He informed me “yes, but they wouldn’t be cool guys.” The kid’s got an aesthetic.

So I tried it a different way, and used it to explain to him the difference between a permutation and a combination. If I told him he could only take 2 out of these 6 creations in the car, he has 15 different groups of two he could select. That’s a combination.

If, however, he has a friend over and I tell them they can take two creations in the car and they each get one, they now have 30 possibilities….the original 15 possibilities x 2 ways of splitting them. That’s a permutation….the order matters in addition to the picks, so the number is always higher.

Of course, they will actually just want the same one, and then we will move on to a lesson in sharing. Also, he’s 5, and he kinda just wandered off part way through permutations and then asked if he could be a baby turtle. That’s when I figured I’d move this lesson to the blog, where I was slightly less likely to get turtle related commentary as a response.

Anyway, the history of using Lego’s to illustrate mathematical concepts is actually pretty robust, and can get really interesting. For more on permutations and combinations, try here.  For why stepping on a Lego hurts so much, try this:

6 thoughts on “Lego Superheroes and Combinatorics

  1. He’s got that New England language quirk of calling females as well as males in a group “guys.”* He won’t get a pass for being woke enough at age five to consider some female superheroes “cool” either. He’s gonna have to unlearn that.

    *Note to non New Englanders. This does not hold in the singular.


  2. Bethany – I can’t believe you are a RACIST! I was doing some research for a political bumper sticker I want to produce and to my amazement, I discovered that your fascination with Combinatorics is racist!

    I’m going to let you try and figure out why I am calling Combinatorics racist. I hope you ROFL when you do. Have a fun weekend.


      • Here’s why.
        Shortly after seeing your post on Combinatorics, I came up with an idea for a political bumper sticker in which the candidates name would be crossed out with the Rebel Flag.
        Not being from “THE South” (apparently growing up in SOUTHern California doesn’t count), I searched for “stars and bars.” The first thing that came up were articles about, you guessed it, Combinatorics, which is apparently best seen by using stars and bars. Therefore if you are interested in Combinatorics you are racist. (Actually at this point if you like to breath you are probably racist, but that’s another screaming match.)
        Naturally, anyone who grew up in THE South know that the “stars and bars” was the FLAG of the Confederacy not the “Rebel flag” which was the Battle Flag. I won’t make that mistake again.


  3. Pingback: I’m Thinking of a Word That Starts With a….. | graph paper diaries

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