B3 A $3 \times 3$ grid of 9 dots labeled by $A, B, C, D, E, F, K, L$, and $M$ is shown in the figure. There is one path connecting every pair of adjacent dots, either orthogonal (i.e. horizontal or vertical) or diagonal. A turtle walks on this grid, alternating between orthogonal and diagonal moves. One could describe any sequence of paths in terms of the letters $A, \cdots, M$. For example, $A-B-F$ describes a sequence of two paths $A B$ and $B F$.

What is the maximum number of paths the turtle could traverse, given that it does not traverse any path more than once?
Answer: 17

Solution: The answer is 17. This is an upper bound because there are 8 possible diagonal moves, hence at most 9 possible orthogonal moves. There are many ways to construct this.

One possibility for a 17-paths trip is $A B D E A D L K E B F E C F L M E L$.