MathDB
Tattoo congress

Source: Russian TST 2016, Day 9 P1 (Group NG), P3 (Groups A & B)

April 19, 2023
combinatorics

Problem Statement

Several people came to the congress, each of whom has a certain number of tattoos on both hands. There are nn{} types of tattoos, and each of the nn{} types is found on the hands of at least kk{} people. For which pairs (n,k)(n, k) is it always possible for each participant to raise one of their hands so that all nn{} types of tattoos are present on the raised hands?