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Congressional seating for SOTU and Discrete Math

Remember when in elementary school when teachers would instruct you to sit “boy-girl-boy-girl?” Well, it appears as if the United States Congress needs to be reprimanded for their childish behavior and must sit “Democrat-Republican-Democrat-Republican.” You see, Colorado Senator Mark Udall made a proposal that during the 2011 State of the Union (SOTU) speech members of congress would sit amongst members of the opposite party. This is in contrast to previous SOTU addresses where the house of congress was firmly divided and after each line half of the house would cheer like their favorite team is trying to make a crucial 3rd down stop and the other half would sit on their hands and scowl. So members of congress accepted Udall’s proposal and immediately members of congress began trying to decide whom to sit next to so they could appear bi-partisan but so as not to sit next to anyone that’s an anathema to that politician’s base supporters (Seriously, they are children).

Anyway, as you may also know, Democrats lost a lot of seats in the 2010 mid-term elections after four years of steady gains. For the 2011 SOTU there were 242 Republicans (Rs) and 193 Democrats (Ds) in the House of Representatives; 53 Ds (and Independents who caucus with the Democrats) and 47 Rs in the Senate. As far as I know, the Senate and Congress sit together during the SOTU, so that’s a total of 289 Rs and 246 Ds.

So upon hearing that Ds and Rs were to sit together at the 2011 SOTU, I wondered a couple things:

  • Is it possible for every member of congress to sit next to a member of the opposite party?
  • If it is possible, how lopsided would the party split have to be before it becomes impossible?

I was hoping this wouldn’t be a simple discrete math problem. And as luck would have it, it isn’t (at least, I don’t think it is). Behold the floor-plan of the House of Representatives.

(note: not actually the floor plan of House of Representatives. At least I don’t think it is. And it certainly isn’t the seats used for the SOTU seeing as there are more members of congress than seats in this diagram. If anyone out there can find a better, more-correct diagram of the seats of Congress during a SOTU please email me. Below, I’ll start out using the entire congress, but eventually I’ll switch to just the House, and then I’ll declare that it doesn’t really matter.)

What a wonderful disparity of seats! There are rows of 15 and rows of two! There are things called the “Republican and Democratic Committee Tables”. And I’ve always wanted to know where the Tally Clerk sits.

So here’s how I would produce this to students.