The second part of your answer is wrong but the conditions you assume seem to be correct. You also intrioduce a variable "both" that I had never thought about before.
Let's see what happens
Pick a farmer at random (unknown to you in advance)
Lets label them L for Liar, T for Truth, and U for undetermined.
If you ask as you propose "which of those two lies SOME of the time"
1)If you ask T, he will say both
2)If you ask L, he will point to T (Other choice is U), but since BOTH (that you introduced) is also a lie, might he not say BOTH? If He is allowed to say both (and why shouldt he be since you allowed T to say both), you are stuck. Either T or Both is a lie and you have learned nothing.
3)If you ask U, he might say anything (and it is irrelevant actually and that is a key, as well as a hint).
The key is YES/NO questions and you have introduced Y/N/B or "him her both" in which both is a potentially acceptable lie that unfortunaltely tells you nothing.
Assuming you got the first half correct (which I had to work thru cause you introduced the answer "both" that I had not thought of), your second question was not correct either.
Try again.
No 3 way answers (Yes No Both).
Has to be, This way that way, this farmer that farmer.
Given that, it should be clear that the second question must yield the way, and the first should weed out the farmer U. It is imperative that U be weeded out.
If U is weeded out, then what single question can you ask a guaranteed liar OR a guaranteed truth teller (no matter which) to find the way?
M |
