# Hmm, this problem seems familiar

**Discrete Mathematics**Level 4

Suppose I have a line of squares, labelled 0, 1, 2, 3, 4, ... 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 \(n\), where \(n\) is a positive integer. What is

\[\lfloor\text{max}(1000X_n)\rfloor? \quad ? \]

If the maximum doesn't exist, find the infimum of the set of \(X_n\).

\[\]**Notation**: \( \lfloor \cdot \rfloor \) denotes the floor function.

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