Problem

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

Tags: combinatorics



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 $A$ acquiring the gift (s) of $B$ without $B$ acquiring the gift (s) of $A$. 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 $A$ will have his gifts and those of a superhero $B$, but $B$ does not acquire those of $A$, but it does keep its own.