# Logic Riddle Puzzle... Torn between two answers

On planet Enigma the inhabitants (called Enigmatics) are either humans or androids (but not both). The androids and humans are indistinguishable by appearance alone. Half the humans always tell the truth and the other half always tell lies. Similarly half the androids always tell the truth and the other half always tell lies Alan arrives on Enigma and overhears the following statements made by Enigmatics at the bar.

If Alan was to immediately deduce each speaker, what would his answer be for each case?

A - "I'm a truthful android"

B - "I'm a lying human"

C - "I'm not a truthful android"

D - "I'm either a truthful android or a lying human"

E - "I'm an android"

To solve this puzzle here is a hint: Even after getting as far as possible to deduce whether the speaker is an android or human as well as whether they might be lying or honest, you still may not always have a definitive answer, but conditional scenario is still a positive answer, for instance:

The speaker x is definitely an android but Alan cannot tell whether the android is honest or dishonest

or

The speaker y is an honest android if the statement is true, otherwise, Alan cannot determine whether speaker y is an android or human

So for speaker A, my friend answered "not truthful human", then when i said she was wrong, she reworded her answer to "it is honest android, or lying human, or lying android" and I proceeded to tell her she was still wrong but she will not stop arguing with me over it.

Based on the entire question up to the hints, my answer was,

If the statement is true, speaker A is an honest android, otherwise, if the statement is false, speaker A is either a lying human or lying android.

Is there really any difference? I think there is based on how the question was framed and how my friends answer is more arbitrary than my own.

• I don't think there's any difference. Just as a matter of taste, I like your friend's first answer best, as the most succinct. Commented Aug 31, 2019 at 4:47
• ur trolling @saulspatz stop it Commented Aug 31, 2019 at 4:49
• What are you talking about? I'm answering your question. Commented Aug 31, 2019 at 4:50
• as a matter of taste? the question even had specific examples of answering... this was a homework problem for advanced logic Commented Aug 31, 2019 at 4:52
• Based on your initial response to @saulspatz, I was actually assuming you were trolling... Note that the "If the statement is true" is equivalent in this problem to "If the speaker is truthful". With this context, your answer is just saying "If speaker A is truthful, then A is an android. If speaker A is lying, then A could be either a human or an android" Now I ask you, what is the difference between that and "A is either a truthful android, a lying android, or a lying human"? What implications can be made with one that can't be made with the other? Commented Aug 31, 2019 at 5:23

## 1 Answer

You both answered the question correctly according to the instructions you were given.

To solve this puzzle here is a hint: Even after getting as far as possible to deduce whether the speaker is an android or human as well as whether they might be lying or honest, you still may not always have a definitive answer, but conditional scenario is still a positive answer, for instance:

The speaker x is definitely an android but Alan cannot tell whether the android is honest or dishonest

or

The speaker y is an honest android if the statement is true, otherwise, Alan cannot determine whether speaker y is an android or human

In this case, your friend correctly noted that $$A$$ can not be a truthful human (because their statement would have been untrue), but that is the most that can be said. That matches the first model response that you were given. You followed the second model and gave a little more information (for instance, if you learned later that $$A$$ also said "Two plus two is four," you could use your analysis to immediately conclude that $$A$$ was an honest android. We can debate whether your friend was more succinct or you were more complete (although we won't debate that here on MSE), but the professor has made it clear that both answers are acceptable for this assignment.