# Organs of the Enterpeton

• Is there an intended "nice" solution to this? You could make any number of these puzzles with different answerers and different characteristics, but does something make this one special?
– Deusovi
Aug 4, 2021 at 18:47

First, it's helpful to create a truth table for the four organs.

Organ Yes? No?
Heart Yes Rand
Lung Rand No
Spleen Rand Yes

Once we have that, we can ask our first question:

The organs will answer like this:

Heart: Either yes or no
Lung: No
Spleen: Yes

Here's what that tells us:

We can ask this second question:

Are you the heart?

Here's how the organs will answer:

Heart: Yes
Lung: No
Spleen: Yes

What does that tell us?

For the third and final question:

Is the year 2021? Only this question, we'll ask multiple times.

Here's how the organs will answer:

Heart: Yes
Lung: Either yes or no
Spleen: Either yes or no

What does that tell us?

Well, after the first time, here's what we'd know:

And how does that get us to our answer?

We've effectively split each organ into one of two organs, and by asking a question that's always true, if we ask it enough times, the organ that answers randomly will eventually answer "wrong" thus eliminating it from the running for the heart/gallbladder (which always answers the same) and proving that it's actually the other organ out of the possibilities. It's faster to ask these three establishing questions first because then the randomization afterwards needs only a 50/50 chance to succeed - we'll probably only need to ask about 4 questions total.

• The problem with this solution is that you cannot be absolutely sure that a random organ will not continue to answer the exact same thing. While the chances are absolutely miniscule; what if you continued asking the question until it was no longer 2021? For that matter, you can't be sure that the organs won't answer whichever answer makes the puzzle most difficult for you and therefore will never change their answer! Aug 4, 2021 at 22:17
• I could definitely replace "Is the year 2021" with "Are you an organ?" or some other always-true answer if we're concerned about that. And, since the original question says that they answer randomly, they cannot answer whichever one makes the puzzle most difficult. Aug 6, 2021 at 15:05
• @TakingNotes since ther organs are allowed to answer randomly, it's possible for them to take the worst-case path, and impossible to rule such cases out. However, the question asked concerns the average case. Aug 14, 2021 at 4:22

To narrow down four possibilities into two, ask this question first:

"Will Spleen lie and Lung tell the truth?"

If yes is correct: Heart says yes, Spleen says no, Lung says yes, and Gallbladder says no.

If no is correct: Spleen tells the truth (which is impossible for a "no" question) and/or Lung lies. So Heart can say anything, Spleen must say yes, Gallbladder can say anything, and Lung says yes (but must say no according to its own rule, which creates a contradiction).

Because of the contradiction, only Yes can be correct, so Heart and Lung will be differentiated from Spleen and Gallbladder.

Then:

To differentiate Heart from Lung, ask "Will Lung or Heart say no?":

If yes: Heart says yes, Lung says no.
If no: Both Heart and Lung say yes, leading to a contradiction.

Because of the contradiction, only Yes can be correct.

Or: