Quentin, Raynor, and Seth work at a grocery store that sells apples, bananas, and oranges.
It is known that precisely two of the men are knights, who always speak truthfully, and the remaining man is a liar, who always tells lies.
They make the following statements:
- Quentin: Seven apples and five bananas cost precisely the same as six oranges.
- Raynor: Four apples and nine oranges cost precisely the same as five bananas.
- Seth: Six oranges and three bananas cost precisely the same as four apples.
Determine the type of each of the three men from the abovementioned clues.
Let a represent price of apples.
Let b represent price of bananas.
Let c represent price of oranges.
Statements:
Q: 7a + 5b = 6c
R: 4a - 5b = -9c
S: 4a - 3b = 6c
Combined:
Q & S: 11a + 2b = 0 Apples and bananas are free.
R & S: 2b = 15c
Q & R: 11a = -3c Either apples or oranges are negatively priced.
Q is the liar; his statement makes impossible implications.
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Posted by Charlie
on 2022-06-25 12:22:32 |
solution
