2024 Author: Malcolm Clapton | [email protected]. Last modified: 2023-12-17 03:44
Find out which tunics the elves are wearing and who beat whom in the curling championship.
The author of this problem is a student from Luxembourg named Lois. He came up with it while sitting in a science lesson. Here is the condition:
Four elves - Glarald, Mnement, Virtana and Tinsel - wear tunics of different colors. At least one of these elves is a liar who always tells only lies. Elves who are not liars always tell only the truth.
The following conversation takes place between them:
Glarald: The moment is dressed in green (1).
Virtana: The elf in green is a liar (2).
Tinsel: I am wearing blue (3).
Glarald: I am wearing yellow (4).
Moment: I am pink (5).
Virtana: The elf in the red tunic beat Tinsel in the elf curling championship last year. I don't play curling (6).
Tinsel: One of us in yellow (7).
Moment: There is only one liar among us (8).
Virtana: I am not dressed in green (9).
Tinsel: At last year's curling championship I was beaten by an elf in red (10).
Q: who beat the elf in the blue tunic at last year's curling championship?
Let's find out what color each elf wears, how many liars there are among them, and who exactly is telling a lie.
1. Suppose Virtana is a liar. Then from statement 2 it follows that the elf in green is not a liar, but from statement 9 - that Virtana is dressed in green. But if Virtana is in green, statement 2 becomes true. This contradicts the assumption that the elf is a liar.
So Virtana is not lying. From this we conclude that she does not wear a green tunic, but one of the elves does.
2. Virtana speaks only the truth. Hence, from statements 6 and 10, we can conclude that Tinsel also speaks the truth. From statement 3 it follows that Tinsel is dressed in blue, from statement 7 - that one of the elves is wearing yellow. It turns out that elves wear tunics in yellow, blue, red and green.
3. We know that no elf wears pink. Therefore, from Proposition 5 it follows that Mnement is a liar, which means that replica 8 is also a lie. It turns out that the elves who tell the truth are Virtana and Tinsel, while Mnemont and Glarald are lying.
4. Tinsel is wearing a blue tunic. Virtana doesn't wear green. From point 1 it follows that Mnement does not wear green either, so Glarald is wearing a tunic of this color. From Statement 6 it is clear that Virtana cannot wear red, she does not play curling. Therefore, Virtana wears yellow, and Mnement wears red.
It turns out that Tinsela, the elf in blue, won the curling championship by Mnement.
Answer: Moment.
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The original problem can be viewed.
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