Intelligence test

[Pyrrho]

Something I cooked up to test your logical thinking skills. Ask any question you feel you need to pertaining to the question.

Two brothers walk up to you.

Man 1 says "One of us tells lies"

Man 2 says "And one of us tells the truth".

Man one states an undeniable fact.

Which one lies, and which one tells the truth?

Determine all of what you know, don't think one has to tell lies and one has to tell the truth.

I read "one of us" as "exactly one of us". The wording is ambiguous.

Hypothesis TT contradicts the first statement, the hypothesis is rejected

TL is compatible with the first statement, but not with negation of statement 2 (none or two of us tell the truth). Therefore the hypothesis is rejected.

LT is compatible with statement 2, but not with the negation of statement 1 (none or two of us tell lies)

LL is compatible with the negation of  statement 1 (none or two of us tell lies) and with the negation of statement 2 (none or two of us tell the truth).

Both are liars therefore is the only consistent constellation.

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Now, if "one of us" is read as "at least one of us" it gets more interesting.

TT is again contradicted by statement 1
TL is contradicted by the negation of statement 2 (none of us tells the truth)
LT is contradicted by the negation of statement 1 (none of us tell lies)
LL is again contradicted by the negation of statement 1 (none of us tell lies).

None of the possibilities remain.

Therefore, we have a Paradox akin to the Barber who shaves everyone except those who shave themselves. Such a barber cannot exist.

Your analysis is good, except that you forgot:

"Man one states an undeniable fact."

With that, both cannot always lie, and so with your first interpretation, none of the options are possible either.

It does not seem to be a well-worded problem.  It seems that they are not both consistent in their answers.