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,b,c be the cost of apples, bananas, and oranges ("c" because oranges have Vitamin C).
Q said: 7a + 5b - 6c = 0
R said: 4a - 5b + 9c = 0
S said: 4a - 3b - 6c = 0
eqns 1&2: 11a + 3c = 0
eqns 1&3: 3a + 8b = 0
eqns 2&3: -2b + 15c = 0
The only way you don't conclude that some item has a negative (or zero) cost is with the last option, so Quentin is the liar
Edited on June 25, 2022, 12:51 pm
|
|
Posted by Larry
on 2022-06-25 12:50:08 |
Solution
