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Date of Award

Fall 1971


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Document Type

Thesis: EWU Only

Degree Name

Master of Science (MS) in Mathematics




High-speed computers can be used to solve many problems that require a large number of tests that satisfy either a positive or a negative requirement. However, the size of the problem that can be handled is limited by the speed and by the accessibility of the computer. Back-tracking is a technique that provides a more efficient method of solving such problems, and thus enables larger problems to he handled.

Chapter I introduces the subject of back-tracking, discusses the general back-t:racking algorithm, and illustrates the technique with an elementary problem in Combinatorial Analysis.In Chapter II, the back-track method is used to solve the Queens problem, a problem of much interest to Mathematicians.

Chapter III states and proves several theorems that resulted from the application of the back--tracking technique to the Queens problem. In Chapter IV, the method is used to solve several problems on the partitioning of numbers. The author leaves the reader with the following conjecture. "There are no non-cyclic pure Latin squares.'