Today we'll learn How to solve the King octopus puzzle

Question

King Octopus has 4 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”

so What is the color of the servant that says the "truth"?

Answer

You might notice that the color of the servant is extra information, at least for solving the puzzle, and is needed only for the answer. The important information is the number of legs each servant has - 6/7/8 and what they say - truth or lie.

Now, how to go about solving it:

since there were 4 servants, we need to make possible groups of different types of servants, in which at least one servant must say the truth, or else the question itself is wrong.

Now the possible groups of 4 servants of 6/7/8 legs are:

1. 4 servants of 6 legs

2. 4 servants of 8 legs

3. 3 servants of 6 legs & 1 servant of 7 leg

4. 3 servants of 8 legs & 1 servant of 7 leg

and so on. you keep making so many such combinations.

Now another restriction on such combinations

since the possible answers given on total legs (25/26/27/28) are different, means only ONE of these four is a correct answer. This indicates only one servant is telling the truth and the other 3 are lying.

What does it mean for possible groups?

You are right. It means 3 servants with 7 legs and 1 servant with 6 or 8 legs.

This means only two right groups are: 7+7+7+6 = 27; and 7+7+7+8 = 29.

29 is not an alternative answer, thus 27 is the right answer.

Which color of the servant said 27? Correct - The Green one.

The answer is "Green" color servant told the truth.