Using the digits in 2011 (one 2, one 0, and two 1’s) and some basic arithmetic operations, generate the integers from 0 to 20. Usually, the operations that can be used in puzzles of this sort are the four basic ones: addition, subtraction, multiplication, and division. You may use these plus factorial and what I will call “triangular”.

*n*! is the product of the integers from 1 to *n*. e.g. 4! = 24. 0! is defined as 1. Without factorial, the 0 in 2011 would be nearly useless. It is a bad century for puzzles like this. “triangular” is is the sum of the integers from 1 to *n*. e.g. 4 triangular = 10.)

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. **The deadline is Wednesday, August 27, 2014 at noon Pacific Time.** I will post the answer shortly after.