Shrinking List Puzzle

By Susam Pal on 17 Feb 2011

The first $$9$$ natural numbers are given in a list. You are supposed to select two numbers randomly from the list, call them $$x$$ and $$y$$, remove them from the list and insert $$x + y + xy$$ into the list. You keep repeating this until you are left with only one number in the list. Find the final number that is left in the list.

See the comments page for the solution.