Other than ordinary farms like Animal Farm, there is a farm called 'Cows Training Farm', which is a farm that trains $15$ very orz cows. Each year, six cows are chosen to join a competition. Mason is now guessing which six cows would enter that competition. If he guesses at least three cows correctly, his guess is said to be accurate. Suppose Mason is smart and has an optimal strategy for guessing. How many times at most would Mason have to guess, such that at least one guess is accurate?
This problem is an unused problem proposed for a relatively unknown small contest, in which I am one of the problem setters and I prefer not to mention that contest here.
Bonus: Try to do this problem when there are more cows. Can you generalize? (I am interested in if there is a good generalization)
This problem is my first problem after one and a half years. Hope you like it!