Electoral Math and Computer Science Rocks!

I wish I taught a computer science course so I could introduce this problem.

How many unique ways are there to acquire at least 270 electoral votes without any excess?

For example, one combination would be to win California, Connecticut, the District of Columbia, Hawaii, Illinois, Maine, Massachusetts, Michigan, Minnesota, New Hampshire, New Jersey, New York, Ohio, Oregon, Pennsylvania, Rhode Island, Vermont, Washington and Wisconsin. That would be equal to 272 electoral votes (not coincidentally, these are the John Kerry states plus Ohio).

Note that there are no excess electoral votes in this combination: if you remove one of the states with three electoral votes, the number falls to 269, which is below the 270-EV cut-off. So winning all of these states plus North Dakota would not qualify, since the candidate has superfluous electoral votes. On the other hand, replacing Vermont with North Dakota would make for a unique combination.

Not only is an awesome math/computer science problem, but I have to say that I totally love the response that it generated in the comments. (Plus, Isabel Lugo’s solution is just so damn sleek.) Minus a minor spat in the comments, this is totally one heck of a sick blog post.



  1. The real issue is that we shouldn’t have battleground states and spectator states of the electoral college in the first place. Every vote in every state should be politically relevant in a presidential election. And, every vote should be equal. We should have a national popular vote for President in which the White House goes to the candidate who gets the most popular votes in all 50 states.

    The National Popular Vote bill would guarantee the Presidency to the candidate who receives the most popular votes in all 50 states (and DC). The bill would take effect only when enacted, in identical form, by states possessing a majority of the electoral vote — that is, enough electoral votes to elect a President (270 of 538). When the bill comes into effect, all the electoral votes from those states would be awarded to the presidential candidate who receives the most popular votes in all 50 states (and DC).

    The major shortcoming of the current system of electing the President is that presidential candidates have no reason to poll, visit, advertise, organize, campaign, or worry about the voter concerns in states where they are safely ahead or hopelessly behind. The reason for this is the winner-take-all rule which awards all of a state’s electoral votes to the candidate who gets the most votes in each separate state. Because of this rule, candidates concentrate their attention on a handful of closely divided “battleground” states. Two-thirds of the visits and money are focused in just six states; 88% on 9 states, and 99% of the money goes to just 16 states. Two-thirds of the states and people are merely spectators to the presidential election.

    Another shortcoming of the current system is that a candidate can win the Presidency without winning the most popular votes nationwide.

    The National Popular Vote bill has been approved by 18 legislative chambers (one house in Colorado, Arkansas, Maine, North Carolina, Rhode Island, and Washington, and two houses in Maryland, Illinois, Hawaii, California, and Vermont). It has been enacted into law in Hawaii, Illinois, New Jersey, and Maryland. These states have 50 (19%) of the 270 electoral votes needed to bring this legislation into effect.

    See http://www.NationalPopularVote.com

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