Answer to Question #87384 in Combinatorics | Number Theory for sayem

Question

1. Daniel chooses some distinct subsets of {1,...... ,2019 }such that any two distinct subsets chosen are
disjoint. Compute the maximum possible number of subsets he can choose.

3. Compute the smallest positive integer that can be expressed as the product of four distinct integers.

Answer 1

1. if we assume that the subsets are non-empty, then answer will be 2019, since every element belongs to only one subset and then we choose all one-element subset
2. 4=(-2)*(-1)*1*2