## Challenge 375: Santa's Seating

Santa is holding a formal party to celebrate the completion of the elves' toymaking for this year!

The party is in an enormous ice cavern near the North Pole which has circular tables that each seat five elves.

Santa has assigned each elf to a particular table, and one table is for five elves named Aster, Bella, Candy, Dusty and Ed.

These days, there are so many elves helping Santa that not all of them know each other's names, but for this particular table Santa knows that if you pick any group of three (a trio) of the elves, there will be one pair both of whom know each other's names and another pair neither of whom know each other's names. (The last pair might know each other's names, or not, or one of them might know the other's name but not vice versa.)

Santa claims that this means that

(i) each elf on this table must know the name of exactly two other elves there

(ii) it is possible for these elves to sit around their circular table so that they know the name of both the other elves they are next to.

Prove that Santa is correct.