Counting Subsets

Mr. Meseeks has just turned evil and is on his way to destroy the universe. To stop him Rick and Morty need to buy some time and keep him busy. So, Morty gives Mr. Meseeks a set A with n elements and tells him to make k non-empty sets B1, B2, … Bk - 1, Bk such that Bk ⊆ Bk - 1⊆ Bk - 2 ⊆…B1⊆ A.

This is a companion discussion topic for the original entry at