What happens when blood of unblemished offerings mixed with blood of blemished offerings? Since this is a common occurrence, the Sages decreed that such blood must be poured into the canal, which ran from the Temple into the adjoining fields. The Sages adopted this decree to prevent a situation where someone may mistakenly rule that there is enough valid blood, whereas in reality the valid blood would be nullified by the invalid one.
What if not the blood, but the cups holding that blood got mixed up? Rabbi Eliezer says that if one cup was already offered, then we can say that it was the blemished one, and offer the remaining ones. The Sages, on the other hand, say that even if all but one were offered, we cannot bring the remaining last one.
Art: William Sidney Mount - Fruit Piece: Apples on Tin Cups