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Let the Nim-sum of all 3 piles be denoted as X.

Let Pile A and Pile B and Pile C contain objects.

( In Nim-Sum )

A + X = D

B + X = E

C + X = F

As we are currently in research of a math project, we are wondering if there is a case whereby D > A, E > B, and F > C. If not, what is the proof?