Four tuple/Modulus of differences/25/Exercise

We consider the mapping

$\mathrm{\Psi }:{\mathbb{N}}^4⟶{\mathbb{N}}^4$

that assigns to a four-tuple $(a,b,c,d)$ the four-tuple

$(|b-a|,|c-b|,|d-c|,|a-d|).$

Find an example of a four-tuple $(a,b,c,d)$ with the property that all iterations ${\mathrm{\Psi }}^n(a,b,c,d)$ for $n\le 25$ do not yield the zero-tuple. Check your result on http://www.vier-zahlen.bplaced.net/raetsel.php .

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