King Octopus and Servants

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 say the truth.

One day, 4 servants met:
The blue one says: “Altogether we have 28 legs”;
The green one says: “Altogether we have 27 legs”;
The yellow one says: “Altogether we have 26 legs”;
The red one says: “Altogether we have 25 legs”.

What is the colour of the servant that is speaking the truth?

Answer

The green one is telling the truth.

Lets assume that one of them is telling the truth and then try to prove that. Since all four servants are disagreeing then 3 of them must be lying.

The servant telling the truth will have either 6 or 8 legs. The other 3 servants will have 7 legs since they lie. So the total number of legs should be either 27 (6 + 7 + 7 + 7) legs or 29 (8 + 7 + 7 +7) legs. Only green servant could be telling the truth as it said 27 legs.

Alternatively, let’s say blue is telling the truth: so the blue one has either 6 or 8 legs. And each of the other octopuses are lying hence have 7 legs each. So our total number of legs: 6 + 7 + 7 + 7 = 27 legs or 8 + 7 + 7 + 7 = 29 legs. But since blue said that altogether they have 28 legs, we know he is lying.

If you follow this same logic for all of them, you realize that only the green octopus can be telling the truth as the number of legs adds up.

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  • Fabella Lector

    There are 4 of them, and we know that they have 6, 7 or 8 legs.
    Blue says 28 legs. Only way that’s possible is if,
    6*1 + 7*2 + 8*1= 28. Since 6 and 8 legs tells the truth, there must be 2 who tell the truth but from the riddle question we know only 1 servant is telling the truth. So, not Blue.
    Green says 27 legs. There are two ways for this:
    1) 6*2 + 7*1 + 8*1= 27, again 3 truth tellers so not possible.
    2) 6*1 + 7*3 + 8*0= 27, only one telling the truth.
    So green is telling the truth.
    Don’t need to bother with the rest since the riddle asked to find the servant (not servants) who is telling the truth.
    ——————————————

    Another way to work this would be. Since only one servant tells the truth, in the 4 you have one who has 6 legs or 8 legs, the other 3 servants would have 7 legs each. Therefor the only possible true answers can be:
    1.) 6*1 + 7*3= 27 legs, or
    2.) 8*1 + 7*3= 29 legs.
    Then you just check the servants responses for one that says 27 or 29 legs to find the one telling the truth. All the others are lies.