@AC and @Matty,
After reading your posts, some deep thinking and 'nitty gritty' analysis,
I must add and make clear a point in the riddle. Both the truth sayer and the liar give responses - either true, or false -
to your question. They present it as a solution to your question. It is either the true solution for what you inquired, or it is a
false solution to your inquiry.
So 'I don't know,' whether said truthfully (he really doesn't know), or said falsely (he knows and is lying), are impossible answers. because they do not present a resolution to your question.
Now, this being the case, they must
know the correct answer to your Q.
Logic - why I am forced to say this -
If the liar can lie by not answering the question, say, with a random lie - 'the sky is yellow,' or with 'I don't know,' (when he does know) then the logic of the correct solution to the riddle fails.
Does Tom lie?
Say you are talking to John. and,
Tom does lie --- so John will truthfully say yes.
Tom doesn't lie - so John is the liar, and he will falsely say Yes tom lies.
but If he can make up gibberish, and not offer a possible resolution to your question (tom lies or doesn't lie), he might make up gibberish like I don't know.
So, so far, John would respond Yes or gibberish. (and not respond no)
If you are talking to Tom, and
Tom is truthful - Tom will say No.
Tom lies, ------- Tom will lie and say No Tom doesn't lie. or make up some gibberish!!
And then if you receive a gibberish response, you know he's a liar, but it is not definitive if its tom or john! it can be both.
So in the riddle when they lie and tell the truth, its as the correct answer to your question. one will present the correct answer. and one will present the incorrect answer as the correct answer.
@AC and @Matty,
After reading your posts, some deep thinking and 'nitty gritty' analysis, [i]I must add and make clear a point in the riddle.[/i] Both the truth sayer and the liar give responses - either true, or false - [b]to your question[/b]. They present it as a solution to your question. It is either the true solution for what you inquired, or it is a [b]false solution[/b] to your inquiry.
So 'I don't know,' whether said truthfully (he really doesn't know), or said falsely (he knows and is lying), are impossible answers. because they do not present a resolution to your question.
Now, this being the case, they must [b]know the correct answer[/b] to your Q.
Logic - why I am forced to say this -
[spoiler] If the liar can lie by not answering the question, say, with a random lie - 'the sky is yellow,' or with 'I don't know,' (when he does know) then the logic of the correct solution to the riddle fails.
[spoiler] Does Tom lie?
Say you are talking to John. and,
Tom does lie --- so John will truthfully say yes.
Tom doesn't lie - so John is the liar, and he will falsely say Yes tom lies.
but If he can make up gibberish, and not offer a possible resolution to your question (tom lies or doesn't lie), he might make up [i]gibberish like I don't know. [/i]
So, so far, John would respond Yes or gibberish. (and not respond no)
If you are talking to Tom, and
Tom is truthful - Tom will say No.
Tom lies, ------- Tom will lie and say No Tom doesn't lie. [i]or make up some gibberish!![/i]
And then if you receive a gibberish response, you know he's a liar, but it is not definitive if its tom or john! it can be both.
[/spoiler][/spoiler]
So in the riddle when they lie and tell the truth, its as the correct answer to your question. one will present the correct answer. and one will present the incorrect answer as the correct answer.
.