TOT 2014 Spring A J4, one king, two wizards, 100 pos. integers
Source:
September 11, 2020
combinatoricsgame
Problem Statement
The King called two wizards. He ordered First Wizard to write down positive integers (not necessarily distinct) on cards without revealing them to Second Wizard. Second Wizard must correctly determine all these integers, otherwise both wizards will lose their heads. First Wizard is allowed to provide Second Wizard with a list of distinct integers, each of which is either one of the integers on the cards or a sum of some of these integers. He is not allowed to tell which integers are on the cards and which integers are their sums. If Second Wizard correctly determines all integers
the King tears as many hairs from each wizard's beard as the number of integers in the list given to Second Wizard. What is the minimal number of hairs each wizard should sacri ce to stay alive?