There are some serious issues in your pageItemCount() solution, so I'd like to give these hints:

• There is a special case named default you can use instead of your construct with an exception. See: https://docs.oracle.com/javase/tutorial/java/nutsandbolts/switch.html
  (but throwing an exception in a helper class which is not specified according to the javadoc, is not a good idea at all. This breaks the rule of "least astonishment".)
• Integer.compare() is not guaranteed to return -1, 0 and 1! compare() delivers either 0, >0 or <0, so -4 could be a valid result as well. See javadoc: http://docs.oracle.com/javase/7/docs/api/java/lang/Integer.html#compare(int,%20int)

Some test cases proposed by @tannah should be added to the problem.

At least these 3

Test.assertEquals(sumStrings('0', '0'), '0');
Test.assertEquals(sumStrings('0001', '002'), '3');
Test.assertEquals(sumStrings('712569312664357328695151392712569312664357328695151392', '1'), '712569312664357328695151392712569312664357328695151393');

I believe, some of these should be added to problem test cases especially

Test.assertEquals(sumStrings('0', '0'), '0');
Test.assertEquals(sumStrings('0001', '002'), '3');
Test.assertEquals(sumStrings('712569312664357328695151392712569312664357328695151392', '1'), '712569312664357328695151392712569312664357328695151393');

I'll file an issue for this