Puzzle | Octopus Empire – GeeksforGeeks

There was an empire where lived a King Octopus with his few servants. The servants either had 6, 7, or 8 legs. It is known that:

•  Seven-legged servants always lied. 
•  6 and 8-legged servants always told the truth. 

One fine day, four servants gathered before the king, and they came up with four statements: 

1. Servant A said, “Altogether, we have 28 legs.” 
2. Servant B said, “Altogether, we have 27 legs.” 
3. Servant C said, “Altogether, we have 26 legs.” 
4. Servant D said, “Altogether, we have 25 legs.” 

How will King Octopus find the truthful speaker?

Solution: As we can see that the four are making different statements and since one of them speaks the truth, three are undoubtedly lying. This forms the base of our argument. 

• Step 1: So, the three lying servants must have seven legs each, resulting in 21(i.e., 7 + 7 + 7) legs. 
• Step 2: Now, the fourth servant speaking the truth must have 6 or 8 legs. Adding 21 to 6 gives 27 legs. Adding 21 to 8 gives 29 legs. 
• Step 3: Since 29 legs are out of the options, hence it is proved that the 27 legs are the correct answer and Servant B is the truthful one.