# Overlapping Squares

**Discrete Mathematics**Level 4

The above consists of \(n\) number of \(2\times2\) squares such that each adjacent \(2\times2\) squares overlap each other on exactly one \(1\times1\) square. And I can only move 1 unit down or 1 unit to the right at a time.

Let \(M_n \) denote the total number paths for me to choose from such that I start the top left point on the top, **X** til I to move to the bottom right point on the bottom, **Y**.

Find \( \displaystyle \lim_{n\to\infty} \dfrac{M_{n+1}}{M_n} \).