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Shylock said:and does that that mean that the formula for max(x,y,z) =
x + (y+z + ly -zl)/2 ?
See for yourself: try (x,y,z) = (1,2,2).
Anyway, max(x,y,z) = max(x,max(y,z)) = (1/2)*[x + max(y,z) + |max(y,z) - x|]. Now substitute the expression for max(y,z).
RGV