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July 24th, 2017, 02:03 AM   #1
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Minimum number of experiments needed

Hello Mathematicians,

My apologies if this isn't in the right thread.

I have an experiment I'm trying to conduct. I won't go into the exact details here but I can easily abstract the problem.

I have six categories of variable x (x1, x2, x3, x4, x5 and x6)

I have four categories of variable y (y1, y2, y3, y4)

I can conduct experiments to find values K. where:

Kab= xa + yb

I wish to find each value of Kab. I know I could run each pair of values in 24 experiments.

However I also know that, for example, I can find K22 by taking K12+K21-K11.

1. What are the minimum number of experiments I need to do to obtain all the 24 values for K?
2. Are there any number of experiments I can do to find the individual values of xn and yn or is this not possible?

Many thanks for your help,

David
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