Reading ARMUT

Difficulty: Hard · Topics: Discrete Mathematics, Combinations, Paths

Starting at the A in the middle of the figure and moving right, left, up or down to a neighbouring letter each time, the word ARMUT is written.

beginarrayccccccccc & & & & T & & & & \\ & & & T & U & T & & & \\ & & T & U & M & U & T & & \\ & T & U & M & R & M & U & T & \\ T & U & M & R & A & R & M & U & T \\ & T & U & M & R & M & U & T & \\ & & T & U & M & U & T & & \\ & & & T & U & T & & & \\ & & & & T & & & & endarray

In how many different ways can ARMUT be formed?