Suppose I have a line of squares, labelled \(0,1,2,3,4, \ldots \) and so on. I place a counter on the square 0. On every turn, I roll a fair die (with the numbers 1 to 6) and move forward as follows: if I was on square \(P\) before the roll and I get a \(x\) then I move to square \(P+x\). Let \(X_n\) be the chance that I land on the square labelled \(n\). Find

\(\text{max}(X_n)? \space\space ( n \in \mathbb{N})\)

and submit your answer as \(n\).

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