Inventory013:  Embedding 5-element metric spaces (proposed by Li Zhou, 11/16/01).

Let d_0 be the maximal metric on R^n, i.e. d_0(x,y)=max{abs(x_j - y_j): j=1,...,n}, where x=(x_1,...x_n) and y=(y_1,...y_n). What is the smallest n such that any 5-element metric space can be isometrically embedded into (R^n, d_0)?

The problem is an one-step generalization of  Problem 681, CMJ  32 (2001), 298-299.  I do not know how difficult the problem is. From CMJ681, we know n=4 is sufficient. I suspect that n=3 would work, but have been unable to manage such an embedding. It seems that such a finite question must be answerable.
 

Discussion.

Bibliography.

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