Problem #56

The way I originally did this one was I made a table,in Mathematica, of all the possible solutions, I then used Notepad++ to place '+'s where I needed them, then finally back to Mathematica to do all of the addition and find the largest of all the values.

If I were to solve this one now, I would use a big integer library (like BigInteger or some other arbitrarily long integer library), then make a function that adds all of the digits together, keep track of the largest one in a variable, and run the loop, outputting the largest one when it is done.