You just bought a package of two dozen oatmeal cookies. Well, you thought you did. It turns out that eight cookies with cinnamon, eight with raisins, and eight with chocolate chips do not make twenty-four if some cookies are counted more than once.
Four cookies have both cinnamon and raisins. Two have both cinnamon and chocolate chips. Three have both raisins and chocolate chips. There are no cookies with all three ingredients.
So how many cookies did you get shorted?
Submit your answer to Gene Wirchenko <firstname.lastname@example.org>. 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 6, 2016 at noon Pacific Time. I will post the answer shortly after.