Enigma 521: Changing truths
14 October 2019
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From New Scientist #1673, 15th July 1989 [link]
As I made my way through the jungle with my truthful guide Lamoura, we came upon a clearing, at the centre of which was a large stone. On the stone were carved the following four sentences:
(A) B is true today and C and D are false today, and D is moon.
(B) An even number of A, B, C, D are false today or C is moon.
(C) B is true today and A and D are false today, and B is moon.
(D) B is true today and A and C are false today, and A is moon.
Lamoura explained that beginning on the morrow and running for the next few days was the festival of the Green Moon. So we decided to camp there until the festival was over.
Lamoura told me that on each day of the festival, each of the four sentences is true or false; she also explained that to say that a sentence is moon means that on at least one day of the festival the sentence is true and on at lease one day it is false.
As each day of the festival dawned, a local native gave me a piece of paper stating which sentences were true that day and which were false. I kept these papers and at the end of the festival, I was able to check that what was written on them agreed with what Lamoura had told me. I also noticed that no two papers said the same thing.
How many days did the festival last, which sentence or sentences were true every day, which were false every day, and which were moon?