King Octopus and His Servants

King Octopus has servants with 6, 7, or 8 legs. The servants with 7 legs always lie, and the servants with 6 or 8 legs always tell the truth. One day four of the king’s servants had the following conversation:

“We together have 28 legs,” said the first octopus.
“We together have 27 legs,” said the second octopus.
“We together have 26 legs,” said the third octopus.
“We together have 25 legs,” said the fourth octopus.

Which of the four servants told the truth?

If all four octopuses lied, then their total number of legs must be 28, which is impossible. Therefore exactly one of them said the truth, and the other three had 7 legs each. Since the truthful octopus must have 6 or 8 legs, and 21 + 8 = 29, we see that it has exactly 6 legs, and therefore it is the second one.

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