Using the digits 2, 0, 1, and 8, and the operations addition, subtraction, multiplication, division, and factorial, form expressions evaluating to the integers from zero to nine. For example, 2 + 0 + 1 + 8 = 11 and (2 + 1) × 8 – 1 = 23. The digits need not be used in the order 2-0-1-8, but you might try anyway. (In other years, I have come up with such solutions for all ten, but for this, I only managed five. Can you do better?)

[Zero factorial (written 0!) equals 1. For a higher integer *n*, *n*! = 1 × 2 × 3 × … × *n*. For example 3! = 6.]

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, January 24, 2018 at noon Pacific Time.** I will post the answer shortly after.