Menachot 106 - One Who Forgot How Much Flour He Promised

We learned before that one who forgot how much flour he promised brings the largest offering, that is, 60 tenths of an ephah. However, Rabbi Yehudah the Prince says that he needs to bring every possible offering between 1 and 60 tenths. Altogether one brings 1830 tenths, which can be calculated by pairing the numbers, 1+60, 2+59, and so on, 30 times (Tosafot). Every toddler mathematician invents this formula, and Gauss did it when his teacher told him to sum up the numbers from 1 to 100.

What is the reason of Rabbi Yehudah? When one brings a large offering and says, "part of it is my obligation, and the rest is a free will offering," he is mixing the two in one vessel, but aaccording to Rabbi Yehudah, mixing obligatory and voluntary offering is not allowed. Alternatively, according to the Sages, he does not consecrate the remainder, and mixing unconsecrated and consecrated items is allowed. However, Rabbi Yehudah argues that then he would be bringing the unconsecrated items into the Courtyard, which is prohibited on its own.

Art: Diego Rivera - Mathematician