Maths Olympiad Prep

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Combinatorics Difficulty 2.7 Junior Find the answer Netherlands

A green, a blue and a red dragon all do not like one of the three vegetables leek, spinach and carrot; each a different one. They also all have a favourite vegetable out of these three, again each a different one. They all make two statements.
* The green dragon says: "My favourite vegetable is leek; the red dragon doesn't like it."
* The blue dragon says: "I don't like carrots; the green dragon does."
* The red dragon says: "I do like spinach; leek is the blue dragon's favourite vegetable."

All dragons have made one true and one false statement.
Which dragon has which favourite vegetable?
A) green: leek, blue: spinach, red: carrot.
B) green: leek, blue: carrot, red: spinach.
C) green: spinach, blue: leek, red: carrot.
D) green: spinach, blue: carrot, red: leek.
E) green: carrot, blue: leek, red: spinach.

This was a multiple-choice question, but the options didn't survive into the source we have. The answer given is B, and the solution below works it through.

Solution

B) green: leek, blue: carrot, red: spinach.

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Source: MathNet, licensed CC-BY-4.0. Statement and solution reproduced as published; topic and difficulty added by this site.