MathDB
2 wizards game, 7 positive integers with sum 100, 4th largest no spoken

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

May 9, 2020
gamegame strategycombinatoricsTournament of TownsToT

Problem Statement

The King gives the following task to his two wizards. The First Wizard should choose 77 distinct positive integers with total sum 100100 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)