Tuesday, December 27, 2016

Introduction to The Outliers of Hyperborea

Now for something a little bit different than knights and knaves:
According to the ancient Greeks, Hyperborea was a land to the north of Mount Olympus, home of the gods. The inhabitants were favored by the gods; they lived for a thousand years in a land of perpetual springtime, and they were free from pestilence.

Little known were the Hyperboreans' unique standards of veracity. Those who lived in the southern region of the land were known as Sororeans and they always spoke truthfully; those who lived in the northern region were known as Nororeans and they always spoke falsely; those who lived in the middle region were known as Midroreans and they made statements that were alternately truthful and false, but in which order was unknown.

There were a few rebels, called Outliers, who disdained the normal conventions of Hyperborea and refused to adhere to the accepted standards of veracity. Their statement patterns as to truth and falsehood were anything that was different from other inhabitants (that is, if three or more statements were made, there were some true statements and some false statements, but not in an alternating pattern).
(Source: Challenging False Logic Puzzles by Norman D. Willis)

For clarification, Midroreans can produce patterns like false, true or true, false when saying two things, or alternatively false, true, false or true, false, true when saying three things etc. (This is of course of little use if the putative Midrorian said only one thing.)

Outliers are even more confounding. Outliers who say one or two things can have any assignment of truth values to their statements imaginable. Consequently, they should be the last choice possible for making conjectures about who is who when they come into play.

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