MathDB

Let

N

be an integer greater than

1

. A deck has

N^3

cards, each card has one of

N

colors, has one of

N

figures and has one of

N

numbers (there are no two identical cards). A collection of cards of the deck is "complete" if it has cards of every color, or if it has cards of every figure or of all numbers. How many non-complete collections are there such that, if you add any other card from the deck, the collection becomes complete?

Problem Statement