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SIMMER

Society Investigating Mathematical Mind-Expanding Recreations

March 1997 Feature Presentation
Introduction to Combinatorial Block Designs
B. Stevens*

We will introduce this topic by looking at three classic problems in recreational mathematics. Then we will delve in to the underlying concepts and look at the answers to some conceptual questions. Finally, we will consider how these ideas fit together in the solution to a fourth and more difficult problem.

  • Three Problems
  • I. The Farmer's Wheat.
  • II. The Schoolgirls' Walk.
  • III. The Tournament Schedule.
  • Delving Into The Concepts
  • Combinatorial Designs.
  • Combinatorial Designs Are Geometries.
  • Resolvable Combinatorial Designs.
  • Kirkman's Schoolgirl Problem
  • References
  • Hints
  • Solutions
    • * Notes edited and modified for SIMMER by Philip Spencer.

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