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Junior Mathematical Olympiad

Netherlands counting and probability

Problem

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.
Solution
B) green: leek, blue: carrot, red: spinach.
Final answer
B

Techniques

Logic