Reading a Palindrome in Several Different Ways
Consider the pseudo-palindrome:
\[WAS IT A CAT I SAW.\]
In how many ways can \(WAS IT A CAT I SAW\) be read if you may start at any \(W\) and move only right, left, up, or down to adjacent letters? Keep in mind that each case can be counted twice since it is a palindrome and that the same letter can be used more than once in each sequence.