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[Community Question] Statistics: Distribution of $\min(X_1+X_2+X_3,X_2+X_3+X_4,X_3+X_4+X_5,X_4+X_5+X_6)$

One of our user asked:

Let $X_{i}\,(i=1,2,3,4,5,6)$ be i.i.d random variables. What will be the distribution of $\min(X_1+X_2+X_3,X_2+X_3+X_4,X_3+X_4+X_5,X_4+X_5+X_6)$?

I just need to know the approach, so any help will be appreciated.


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