# Shrinking Squares.An empirical exploration

Level pending

Start with a sequence $$S=(a,b,c,d$$ of positive integers and find the derived sequence $$S_{1}=T(S)=(|a-b|,|b-c|,|c-d|,|d-a|$$.Define a sequence $$S,S_{1},S_{2}=T(S_{1}),S_{3}=T(S_{2}),...$$.

Let $$S_{i}$$ minimizes the sum of the four elements.What is the sum of the four elements of $$S_{i}$$?

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