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? combinatoricscombinatorics proposed