perplexus.info :: Liars and Knights : Graduation Day

Graduation Day (Posted on 2005-04-18)

It's Graduation Day at LKU (Liars and Knights University) where everyone enrolled is either a Liar (who always lies) or a Knight (who always tells the truth). You approach four youths who just received their diplomas, two of whom are Liars and two of whom are Knights. It is known that each of the four majored in a different one of four subjects and minored in a different one of the same four. Each makes three statements:

Roberta:
   1. Friedrich did not minor in botany.
   2. Either Gloria or myself or both took philosophy.
   3. Both girls either majored or minored in botany.

Gloria:
   1. Between them, Melrose and Roberta took all four classes.
   2. I did not minor in botany.
   3. Roberta is a Liar.

Melrose:
   1. I majored or minored in math.
   2. Friedrich is a Liar
   3. Roberta majored in history.

Friedrich:
   1. Melrose did not major or minor in math.
   2. I majored or minored in philosophy
   3. Gloria minored in math.

Which are the Liars and the Knights, and what did they major and minor in?

Submitted by Captain Paradox

Rating: 4.0000 (6 votes)

Solution: (Hide)

Robert and Melrose are either both Liars or both Knights. Gloria and Friedrich are either both Liars or both Knights.

Let's start by assuming that Roberta and Melrose are Knights and Gloria and Friedrich are Liars.

Gloria must have minored in botany. Roberta must have majored in botany. Melrose majored in history and minored in philosophy. Since Friedrich did not major in philosophy (his second statement) Gloria must have, and the only subject left for Friedrich's major is mathematics. Thus Roberta minored in math and Friedrich minored in history.

But this is impossible since Melrose must have majored or minored in math (R2). Thus Roberta and Melrose must be Liars and Gloria and Friedrich must be Knights.

From here it's not very hard. Gloria minored in math. Friedrich minored in botany. Friedrich majored in philosophy and Roberta minored in philosophy. Melrose must have minored in history, and since both his subjects are different from Roberta's, Gloria must have majored in history. Melrose did not take math, so he majored in botany, and Roberta minored in botany.

The end result is:
Roberta, math, philosophy
Gloria, history, math
Melrose, botany, history
Friedrich, philosophy, botany.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-02-22 00:09:40
Eric's solution is correct - posted official one is not.	Matt	2005-06-16 17:52:24
re: Solution - spoiler	Trish	2005-04-18 22:53:20
Step by Step Solution	Eric	2005-04-18 19:05:51
First thoughts...	Federico Kereki	2005-04-18 17:43:53
Solution - spoiler	Erik O.	2005-04-18 17:42:40

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