There are many categories of questions which cannot be resolved. Some are labeled "Tiyuvta," meaning that the fact that there is no answer led to the conclusion that the previous understanding was wrong. Some are labeled "Kashya," meaning that there is a difficulty with a previous understanding but it could be resolved. Other questions are labeled "Teiku. The Gemara intends to say that these questions do not contradict a previous understanding but cannot be resolved in any known way. The word "Teiku" can be read as an acronym for "Tishbi Yetaretz Kushyos u'Be'ayos" -- "Tishbi (Eliyahu ha'Tishbi) will resolve questions and problems" (see Tosfos Yom Tov, Eduyos 8:7), but it could also be translated as the Aramaic for "let it stand," meaning let the question stand as it is.

In monetary situations this would seem to imply that we apply the rule of ha'Motzi me'Chaveiro Alav ha'Re'ayah (one who wishes to extract from his friend must bring proof), and therefore the claimant will not receive money in these cases. This is the opinion of the Ri (Tosfos Nedarim 91a, Bava Kama 62a). However, other Rishonim (Rif, Rav Hai Gaon) maintain that in such monetary situations each party swears and takes half of the claim.

When Teiku involves a matter of Isur and not monetary issues, the rule is that we are stringent (Rashi, Chulin 30b, 45b; Rif, Berachos 17a), unless it is a rabbinic prohibition in which case we are lenient (Ritva, Shabbos 65a, Moed Katan 4b).

It is related that a certain person answered all of the Teiku questions and came to the Vilna Gaon for an approbation but was told that Teiku implies that human intelligence cannot answer these questions.

Yoel Domb