Question 54
A hundred quadratic envelopes, each of different size, are arranged in a way that, for every two different envelopes, the smaller one is either inside of the bigger one, or they are outside of each other. At the same time, in both of the envelopes there can be other envelopes. Two arrangements are considered different if there are two envelopes which are inside each other in one of the arrangements, while being outside of each other in the other arrangement.
How many different arrangements are there such that the biggest envelope contains all the remaining envelopes? (Richard Stanley's problem set)
How many different arrangements are there such that the biggest envelope contains all the remaining envelopes? (Richard Stanley's problem set)