### Demo of Latin Square design for high school chemistry class

James N. Cawse of GE Global Research emailed me this week with this question.

"Mark, has anyone developed a demonstation/experiment suitable for high school students that illustrates a Latin Square design? I've been asked to give a high school chemistry class on combinatorial chemistry; as I thought about it, the simplest "combinatorial" type design is a Latin Square. It actually has a chance of being understood because of the current craze for Sudoku."

My response was:

"James, Funny you should mention Sudoku and Latin Squares because this morning I was thinking how the same structures apply to Latin Hypercube Designs (LHD) that are popular for DOE on computer sims, for example ones based on finite element analysis that GE uses for designing jet and power turbines. (An aside -- I just got the Jan-Feb issue of American Scientist featuring in their Computer Science column an article titled "Unwed Numbers" on the mathematics of Sudoku. This name stems from the Japanese firm Nikoli who called these puzzles "the numbers must be single" in the sense of being unmarried.) To answer your question, no I don't know of a classroom experiment that illustrates the Latin Square structure."

If any of you StatsMadeEasy blog readers knows of good in-class chemistry experiments that illustrate Latin Square or other principles of DOE, post a comment.

PS. I see that Wikipedia offers a very extensive entry for Sudoku that includes this comment about the mathematics of it:

"A valid Sudoku solution grid is also a Latin square. There are significantly fewer valid Sudoku solution grids than Latin squares because Sudoku imposes the additional regional constraint. "

"Mark, has anyone developed a demonstation/experiment suitable for high school students that illustrates a Latin Square design? I've been asked to give a high school chemistry class on combinatorial chemistry; as I thought about it, the simplest "combinatorial" type design is a Latin Square. It actually has a chance of being understood because of the current craze for Sudoku."

My response was:

"James, Funny you should mention Sudoku and Latin Squares because this morning I was thinking how the same structures apply to Latin Hypercube Designs (LHD) that are popular for DOE on computer sims, for example ones based on finite element analysis that GE uses for designing jet and power turbines. (An aside -- I just got the Jan-Feb issue of American Scientist featuring in their Computer Science column an article titled "Unwed Numbers" on the mathematics of Sudoku. This name stems from the Japanese firm Nikoli who called these puzzles "the numbers must be single" in the sense of being unmarried.) To answer your question, no I don't know of a classroom experiment that illustrates the Latin Square structure."

If any of you StatsMadeEasy blog readers knows of good in-class chemistry experiments that illustrate Latin Square or other principles of DOE, post a comment.

PS. I see that Wikipedia offers a very extensive entry for Sudoku that includes this comment about the mathematics of it:

"A valid Sudoku solution grid is also a Latin square. There are significantly fewer valid Sudoku solution grids than Latin squares because Sudoku imposes the additional regional constraint. "

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