MathDB

Snow White and the Seven Dwarves are living in their house in the forest. On each of

16

consecutive days, some of the dwarves worked in the diamond mine while the remaining dwarves collected berries in the forest. No dwarf performed both types of work on the same day. On any two different (not necessarily consecutive) days, at least three dwarves each performed both types of work. Further, on the first day, all seven dwarves worked in the diamond mine.
Prove that, on one of these

16

days, all seven dwarves were collecting berries.

Problem Statement