Chapter 6 - Section 6.3 - Decision Algorithms: The Addition and Multiplication Principles - Exercises - Page 426: 49c

Infinite number of routes

If we allowed left and up moves too, there would be infinite possible routes because we could go in a small circle (for example the middle four squares) for a number of times, and then go to the finish. It will be a different route if we do 1,2,3...46... circles