Let n be a positive integer. There is a collection of cards that meets the following properties:
∙Each card has a number written in the form m!, where m is a positive integer.
∙For every positive integer t≤n!, it is possible to choose one or more cards from the collection in such a way
that the sum of the numbers of those cards is t.
Determine, based on n, the smallest number of cards that this collection can have. combinatoricsnumber theory