# But the average roll is 3.5

Discrete Mathematics Level 4

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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