MathDB

Let

n

be a given positive integer. A restaurant offers a choice of

n

starters,

n

main dishes,

n

desserts and

n

wines. A merry company dines at the restaurant, with each guest choosing a starter, a main dish, a dessert and a wine. No two people place exactly the same order. It turns out that there is no collection of

n

guests such that their orders coincide in three of these aspects, but in the fourth one they all differ. (For example, there are no

n

people that order exactly the same three courses of food, but

n

different wines.) What is the maximal number of guests?

Problem Statement