GAUSS8 2018 Problem 25

In the 2 \times 12 grid shown, Ashley draws paths from A to F along the gridlines.

In every path,

  • there are two or more arrows arranged head to tail,
  • the tail of the first arrow starts at A and the head of the last arrow ends at F,
  • two consecutive arrows must be perpendicular to one another,
  • no two arrows can intersect at more than one point, and
  • all arrows have different lengths.

The path from A to F shown consists of arrows of three different lengths: left 2, up 1, right 11. How many different paths are there from A to F ?

Answer Choices
A. 54
B. 55
C. 56
D. 57
E. 58