A Sprouts Document from 1974

June 6, 2010

Of Nim and Sprouts, by Curtis F. Hatfield, is a 25 page typewritten manuscript owned by Minnesota State University, Mankato. Since it is obviously an unpublished, one-of-a-kind item, I am a bit surprised that I was able to borrow it through interlibrary loan, but I am glad to have had the opportunity to satisfy the curiosity I felt when a reference to it popped up on a search of

The paper is an academic exercise, a report presented in Mathematics 6882, a graduate-level seminar at Mankato State College, in the spring of 1974. The sprouts content is brief, an attempted exhaustive analysis of n = 2 in two pages of hand drawn diagrams. This analysis actually has a serious flaw, claiming a win for Left, a circumstance which we might say goes to show the pitfalls even an advanced student of mathematics can succumb to in sprouts when not armed with the survivor concept or a system of sprouts notation. The main goal of this part of the paper seems to be to illustrate the game theoretic concept of saddle point.

The greater part of the paper, page nine onwards, is a detailed exposition of the nim algorithm. Despite the title of the paper, this algorithm is not related back to sprouts.

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