How to refactor an application with multiple switch cases?

I have an application which takes an integer as input and based on the input calls static methods of different classes. Every time a new number is added, we need to add another case and call a different static method of a different class. There are now 50 cases in the switch and every time I need to add another case, I shudder. Is there a better way to do this.

I did some thinking and came up with this idea. I use the strategy pattern. Instead of having a switch case, I have a map of strategy objects with the key being the input integer. Once the method is invoked, it will look up the object and call the generic method for the object. This way I can avoid using the switch case construct.

What do you think?