First ask who are all the 4 togglers point to them in your answer, then ask who is the truthteller and point to them. This is presuming that the togglers must know all information that's required and must strictly follow the truth/lie or lie/truth oscillation and can alternate within the same question by distinct sentences,
without invoking a contraction within one or two statements adjoining and thereby violate the rules (like they can't say two lies in two statements in a row or have a half-truth answer, must be truth or lie) and can be allowed to answer by pointing instead of talking (but even with talking it's still possible too).
I've invoked a contradiction of rules if he tries to start with a lie/truth with a four statement method; because the toggler will be forced to tell the truth two statements in a row (as there's only one truthteller, and I'm asking for
four inputs). Even if they try to break the statements into three statements, it must strictly be truth-lie-truth to not invoke a contradiction, and the second answer is virtually unnecessary. No matter how he does it he cannot do it without invoking a truthful statement at some point and cannot proceed with that method of purely lying.
The only way they can avoid this contradiction other than what I corrected before is to cite all the names as one or two statements, and be forced to be truthful with one of them about it. However trying to play it as two statements will look awkward and why would you single out a person from a explicit list? He can only say, "Those three. Oh him as well" basically. So depending on whenever or not it's one, two or three statements:
* If he says, "Oh it's him, him, him, him" as one statement (bear in mind this can only be truthful), then the second answer will show a contradiction by citing the same name twice and the one never mentioned is the truth teller. But you don't even really need the second answer anyway because he's forced to confess he's one too using this method. The second question is merely insurance.
* If he says, "Oh it's him, him, him. Also him too" as two statements, the singled out person is the truthteller and the second answer isn't really necessary but to confirm the person I'm talking too isn't the truthteller, but then the phrasing of statements alone shows him obeying the toggler rule anyway.
* If he says, "Oh it's him, him. Also him. Also him" as three statements, and he attempts to say he's the truthteller why did he need to split up those names? So it's obvious he's lying and thus the truth teller is the middle statement as the first and last statements must be truths, the other way around results in a contradiction of rule. The same applies if he says any other name because of the way he phrased those statements, and it
must follow the truth-lie-truth sequence to not contradict the rules.
By statements, I presume you mean they must be like sentences, and thereby noticeably separate or that's just cheating.
However, in the Truthteller's case, he'll tell me who the others togglers are as one unbroken statement and himself is the truthteller without trouble or invoking a contradiction.
I think I broke/solved the brainteaser by accident by trying to be a smartass.
