In the diagram below, how many unique paths are there that spell the word "KAYAK"?
*You may begin at any K and end at any K
*You may only pass from one letter to a letter in an adjacent hexagon
*Since KAYAK is a palindrome, each path has a corresponding path moving in the opposite direction -- count these as two separate paths!
*Each path must contain 5 different hexagons -- so, for example, you cannot use the same letter "A" twice in one spelling