Question 2
The figure below shows a grid of $10$ squares in a row. Each square has a diagonal connecting its lower left vertex to its upper right vertex. A bug moves along the line segments from vertex to vertex, never traversing the same segment twice and never moving from right to left along a horizontal or diagonal segment. Let $N$ be the number of paths the bug can take from the lower left corner $(A)$ to the upper right corner $(B).$ One such path from $A$ to $B$ is shown by the thick line segments in the figure. Find $\sqrt{N}.$
