MathDB

5

Part of OIFMAT I 2010

Problems(1)

gifts among 5 superheroes and sorcerer Vicencio

Source: OIFMAT I 2010 day 2 p5 - Chilean Math Forum FMAT Olympiad https://artofproblemsolving.com/community/c2484778_oifmat

9/25/2021
The vigilantes are a group of five superheroes, such that each one has one and only one of the following powers: hypnosis, super speed, shadow manipulation, immortality and super strength (each has a different power). On an adventure to the island of Philippines, they meet the sorcerer Vicencio, an old wise man who offers them the following ritual to help them: The ritual consists of a superhero AA acquiring the gift (s) of BB without BB acquiring the gift (s) of AA.
Determine the fewest number of rituals to be performed by the sorcerer Vicencio so that each superhero controls each of the five gifts.
Clarification: At the end of the ritual, a superhero AA will have his gifts and those of a superhero BB, but BB does not acquire those of AA, but it does keep its own.
combinatorics