My Math Forum Minimum number of experiments needed

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 July 24th, 2017, 02:03 AM #1 Newbie   Joined: Jul 2017 From: Liverpool Posts: 1 Thanks: 0 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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