Oh, look at the puppies! They are so cute. There are seven of them. Despite being young, they have already developed personalities. Five of them most definitely enjoy chewing on rawhide chewtoys. Three of them like chewing on slippers. Four of them are scrappers and like chewing on each other.
1) Is it possible for each puppy to have at least two preferences?
2) What is the maximum number of combinations of preferences that can be had by at least one puppy? And the minimum?
3) As in #2, but each puppy must have at least one preference?
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, December 10, 2014 at noon Pacific Time. I will post the answer shortly after.