Grandma is making oatmeal cookies. She is making a batch of 36. To the basic recipe, she adds apple sauce, chocolate chips, and cinnamon in various combinations.
1) The numbers of cookies for one of the ingredient’s four combinations are consecutive e.g. 7, 8, 9, 10.
2) All of the apple sauce combination numbers are prime.
3) The number of cookies with exactly two of the additional ingredients is as big as it can be.
4) The number of cookies that have chocolate chips is even.
5) Each combination of additional ingredients has a different number of cookies.
6) The number of cookies that have cinnamon is prime.
7) There is only one cookie with none of the additional ingredients.
8) There is at least one cookie in each of the eight possible combinations.
Submit your answer to Gene Wirchenko <email@example.com>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, March 11, 2015 at noon Pacific Time. I will post the answer shortly after.