Octopodes
King Octopus has servants with six, seven, or eight legs. The servants with seven legs always lie, but the servants with either six or eight legs always tell the truth.
One day, four servants met.
The first one says, “Altogether, we have 28 legs.”
The second one says, “Altogether, we have 27 legs.”
The third one says, “Altogether, we have 26 legs.”
The fourth one says, “Altogether, we have 25 legs.”
If only one is telling the truth, how many legs do they have altogether?
The answer is 27.
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1 solution
First: One of them tells truth. Indeed, if we suppose that all of them lie, then all of them have 7 legs, which makes the 1st a truth-teller. But, only one statement can be true. So that there is exactly one truth-teller. Second: The truth-teller has 6 legs. Indeed, a liar has 7 legs, so if the truth-teller has 8 legs, then they have 3*7+8=29 legs in total and all lie. Third: Now we just add 3 x 7 + 6 = 27.