The Fight
Two among Anthony, Bernard and Charles are fighting each other.
The shorter of Anthony and Bernard is the older of the two fighters.
The younger of Bernard and Charles is the shorter of the two fighters.
The taller of Anthony and Charles is the younger of the two fighters.
Who is not fighting?
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1 solution
A - Antony B - Bernard C - Charles
First, assume A is not fighting. Making both B and C to be fighters. Using the third data, the younger of B and C (both fighters) is the shorter fighter. Let us use the fourth data, the taller of A and C (only C is the fighter) is the younger fighter. We can assume that A is the shortest of the three. And using the second data, the shorter of A and B (only B is the fighter) is the older fighter, but we already concluded that A is the shortest of the three and our assumption is A is not a fighter. Therefore A is a fighter.
Next, assume B is not fighting. Making both A and C to be fighters. Using the second data, the shorter of A and B (only A is the fighter) is the older fighter. We can conclude that A is older than C and A is shorter than B. Let us use the third data, the younger of B and C (only C is the fighter) is the shorter of the fighter. It will then make C the shortest and the youngest of the three which contradicts the fourth data, the taller of A and C (both fighters) is the younger fighter. Therefore B is a fighter.
Obviously, C is not a fighter but let us check anyways. (Or you can assume C is not fighting in the first place.)
Assume that C is not fighting. Using the third data, the younger of B and C (only B is the fighter) is the shorter fighter, we can say that B is shorter than A and B is younger than C. Using the second data, the shorter of A and B (both are fighters) is the older fighter, we can say that B is older than A. Using the fourth data, the taller of A and C (only A is the fighter) is the younger fighter, we can say that A is younger than B and A is taller than C. The data fits well but let us arrange their age and height from greatest to least for checking purposes.
B is shorter than A B<A (h) B is older than A B>A (a) B is younger than C B<C (a) A is taller than C A>C (h)
Answer. C - Charles is not a fighter.