The Fight
Two of Anthony, Bernard, and Charles are fighting each other.
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The shorter of Anthony and Bernard is older of the two fighters.
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The younger of Bernard and Charles is shorter of the two fighters.
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The taller of Anthony and Charles is the younger of the two fighters.
Who is not fighting?
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1 solution
In the first statement, assume that Anthony is shorter than Bernard. This means that Anthony is the older of the fighters. Now, in the last statement, Anthony cannot be taller than Charles, because he cannot be the youngest of the fighters. This means that Charles is taller than Anthony, and that Charles and Anthony are the two fighters. But now, the middle statement, because Bernard isn’t fighting, states that Charles is the shorter of the fighters. But we already know that Charles is taller than Anthony, so this is a contradiction .
So, in the first statement, Bernard must be shorter than Anthony, and therefore the oldest of the fighters. Now, assume that Bernard is older than Charles. The second statement states that Charles would therefore be the shorter of the two fighters, and therefore, shorter than Bernard. This then makes him taller than Anthony in statement three. However, Charles cannot be shorter than Bernard but taller than Anthony because Bernard must be shorter than Anthony, so this is a contradiction .
Now, assume that Bernard is younger than Charles. The second statement makes Bernard the shortest of the two fighters. However, Charles cannot be the other fighter, because he is older than Bernard, and Bernard is the oldest fighter according to the first statement. So Anthony must be the other fighter. We know Anthony is taller than Bernard, and if he is the fighter, he is also the youngest fighter. We find no contradiction here, so Charles is the one not fighting.