You are right. It’s 12 or more different kinds of pizza. If it was 1 kind of pizza served, he could be certain, that one kind of pizza was at the majority (in that case at all minus one) orders. Since somebody could order a salad. But only one without pizza, to avoid equal orders by pizza kind.
Even if there were 11 different pizza kinds on the menu, Marco could be sure, there is the majority kind of pizza there. Since this Fraenkel conjecture has been proved up to 11 by now.
But for 12 or more, no one really knows yet. Probably it’s true, but who knows. Congratulation, you were rather quick. Despite the fact, the problem formulation looks vague to you.
You are right. It’s 12 or more different kinds of pizza. If it was 1 kind of pizza served, he could be certain, that one kind of pizza was at the majority (in that case at all minus one) orders. Since somebody could order a salad. But only one without pizza, to avoid equal orders by pizza kind.
Even if there were 11 different pizza kinds on the menu, Marco could be sure, there is the majority kind of pizza there. Since this Fraenkel conjecture has been proved up to 11 by now.
But for 12 or more, no one really knows yet. Probably it’s true, but who knows. Congratulation, you were rather quick. Despite the fact, the problem formulation looks vague to you.
I searched for <<family of subsets closed under union “more than half”>> and the Wikipedia page about the conjecture was the first result :-).
It’s nothing wrong with the Googling method. Besides, one could search for <<pizzeria at the end of the world papa mamma>>. Should work now, too.
Maybe, next year’s solution to this problem will be “at least 13”.