Problem

Source: Tournament of Towns, Junior A-Level , Spring 2019 p1

Tags: game, game strategy, combinatorics, Tournament of Towns, ToT



The King gives the following task to his two wizards. The First Wizard should choose $7$ distinct positive integers with total sum $100$ and secretly submit them to the King. To the Second Wizard he should tell only the fourth largest number. The Second Wizard must figure out all the chosen numbers. Can the wizards succeed for sure? The wizards cannot discuss their strategy beforehand. (Mikhail Evdokimov)