Wednesday, July 25, 2012

The Combinatorics of Batman

(I wrote this post about a year ago but waited until the new Batman
movie came out to post it. I haven't seen the movie yet so
there may more possibilities to add to this.)

There have been many versions of the BATMAN story:
comic books (and within that there are several versions),
many movies, and a TV series.
This may lead to a COMBINATORICS question you can ask your class.

So how many ways can the BATMAN story go?
This is NOT A QUIZ- all of the answers are correct
for some version of BATMAN.

1) As a child Bruce Wayne saw his parents gunned down.  What were they doing before this happened?

 a) Watching the movie Zorro.
 b) Watching the movie The Lone Ranger.
 c) )Watching an Opera.

2) Who shot Bruce Wayne's parents?

 a) Joe Chill- a low level mugger.
 b) Joe Chill- hired by the mob since Thomas Wayne (Bruce Wayne's father) had once foiled a crime. The orders were to leave the boy alive so it would look like a low level mugging.
 c) The gangster who would later become the Joker.

3) Who was the Joker before he became the Joker?

 a) A completely innocent chemist-turned-comedian.  He was a good man but a bad comedian. He was just going to do one theft to make ends meet. Things went wrong and he fell into a batch of chemicals and became The Joker.  He is now a bad man but a good comedian.
 b) A gangster who was sleeping with his bosses girlfriend.  The boss arranged for him to be killed ,but nstead the gangster falls into a batch of chemicals and becomes The Joker.
 c) Hey, its just makeup. But he has scars which may have come from his father, himself, or who knows?
 d) There are surely other versions I do not know.  One could probably write a bad PhD on this topic.

NOTE: I don't think the Jokers name is known in any of the versions.
(Contrast: The Riddler's name is Edward Nigma.)

4) Where is the Joker now?

 a) In Arkam Asylum.
 b) Dead.
 c) Gee, he really seemed to die but we just know he'll turn up again.

5) Who is Two-face?

 a) Harvey Dent, the DA, who was a good man. During a court trial a criminal throws  acid on his face. Now half of his face is scared. This drove him insane and he is now a criminal.
 b) Harvey Dent, the DA, who was a good man. Dent and his girlfriend Rachel Dawes are kidnapped.Batman and Commissioner Gordan save him but (1) Rachel dies, and (2) Dent has his face half disfigured.This drives him mad.
 c) There are about 5 other people who took on this role. One of them was named Harvey Kent.   No relation to Clark Kent

6) Who else lives in Wayne Manor?

 a) Robin, Alfred the Butler, and Aunt Hariet.
 b) Robin and Alfred the Butler.
 c) Just Alfred the Butler.

7) How well do Batman and Superman get along?

 a) Superman is never mentioned.
 b) They get along.
 c) They don't get along.
 d) They REALLY don't get along!

This leads to a combinatorics question and a Batman question.
COMBINATORICS: Assuming that all of these options are independent, how many versions of the
Batman Legend could there be? This should be easy.
BATMAN: Of all of these, how many have actually been realized?
This might take a Batman scholar to figure out.
And I haven't even talked about Robin (nor will I).

There are also variants of the COMBINATORICS question if you disallow certain
combinations. For example, If Aunt Hariet exists then Superman does not.

I'm sure there are more options I don't know about.
If you know any, comment!


  1. The Joker's name is known in several of those iterations that you mention: In the Tim Burton version his original name is Jack Napier (played by Jack Nicholson); as the Red Hood (the Chemist turned criminal) I think his "real" name was Joe Kerr (get it?).

    I think the real answer is: there are a countably infinite number of ways you can do the Batman story: just think up a new angle and go with it (or rehash, recombine old angles). Its what they've been doing for the last 60 years after all.

    BTW: your examples seem to have a heavy bias toward the TV and film versions; there are a LOT more combos when considering 60 years of comic archives.

  2. Oh man, this is a fun question. But most of the plot points you mention function independently from one another in the comics - meaning there are few books which reference both the origin story of Batman and the origin of the Joker together, so you'd have to allow the possibility that many of those options can coexist, even if they aren't explicitly said to. I will be thinking about this and rereading Batman comics all day now.

    1. Maybe publish an article in the International Batman Journal. How does one references a comic book though? :P

  3. If 2(a) is from "Batman Begins" then it should be noted that Joe Chill was implied to have been a hired hit there too. Listen to the dialog with Ra's in the mansion.

  4. Don't forget the Batgirl variations or the versions of Huntress or Harley Quinn or any number of characters who have multiple versions. They "explain" this with the existence of multiple Earths. They merged them a while back into a single one with characters merging several realities and even memories. The Earths are numbered with positive integers.

  5. If you read the entry on Batman (or Joker or others) on Wikipedia
    you get a sense of just how complicated an convulted the comic book universe is. DC comics had the merge to clean things up and be able
    to restart things. They also rebooted Superman (and probably others) so that they don't have to worry about continuity with
    issues from the 1940's.

    Marvel comics does not have as many versions of things within the comic but they do have the time-problem. Peter Parker was in High School in the early 1960's, so he should be about about 60 now.
    And his Aunt May has been in bad health for all of that time also- she should be over 100 surely.

    Unlike Mathematics, Comics need not be consistent.

  6. Comic books have clones (often evil).

    Mathematics has the Banach-Tarski paradox.