Posted by: khuang01 | December 10, 2008

A Magical Space of Squares

Hey Everyone,

You can read my Reading Project report on “Marriage, Magic and Solitaire” by David Leep and Gerry Myerson (1999) here.




  1. You were surprised that semi-magic squares form a vector-space as described in the paper. It is an interesting space, and an example of how mathematics can be creative. Vector spaces are ubiquitous, in fact, for two reasons. First, because to be a vector space is actually a fairly lax condition, once you have a field at hand. A class of objects defined by a property forms a vector space if that property is preserved under addition and scalar multiplication. Second, because linear algebra is so powerful, people always look for ways to make vector spaces out of anything they want to understand. We understand linear algebra very well (at least compared to other areas of mathematics) and so if we can translate a problem we wish to solve into linear algebra, we can usually understand it much better.

    You have a mistake in your statement of Hall’s marriage principle (beginning of the second line, the union is over j in J but not OF anything), and some inaccuracies in the discussion immediately following.

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