Intelligence test

[Alex K]

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. (edit: and I for now ignore the additional comment, c.f. Pyrrho) (edit: I also read them as meaning "always, consistently" c.f. Losty)

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. (edit: however, this constellation is not compatible with the additional comment about the undeniable fact. The riddle in this reading is inconsistently written, c.f. Pyrrho)

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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 [Russell] who shaves everyone except those who shave themselves. Such a barber cannot exist, or there is a limitation of the language used in which no truth value can be assigned to some sentences.