In a group of 2n schoolchildren each one has at least n friends. On an outing, the teacher tells them to hold hands in pairs. Show that this can be done with each child holding a friend’s hand, and that if n > 1, the choice of friends can be made in at least two diﬀerent ways.

This was on a previous exam, and I have yet to receive the solutions for it. Can anyone help? 


Question: Is there a list of Mitzvot and their corresponding body parts?
Answer: There is a little known Chassidic text published in 1834 entitled Pri Yitzchak that details all 613 Mitzvot and the corresponding limbs for positive mitzvot and 365 Gidim for negative commandments. It has not been translated from the Hebrew. It is a very sophisticated work. 

He uses the list of halachic limbs listed in the Mishna, and uses the Rambam's list of the 613 Mitzvot.

The Sefer was written by R' Yitzchak ben R' Tzvi Hersh, the Rav of the city of Shkod(?) and published by his son, Shabtai Sheptel, some years after his passing.  

The first 40 pages are available for free online, thanks to Otzar Hachachma (The other 20 are also available, but must be paid for). 

In the introduction, R' Yitzchak lays out the guidelines he used to develop this work. At the end of the introduction he says that while some of the Mitzvot and their corresponding limbs were found in various Sefarim, the majority of them were not. He decided which Mitzvot corresponded to which limbs, and as such, the list should not be considered definitive. The intent of the Sefer is to be used as a memory aid, increase the readers love and fear of G-d, and so the reader can realize how the soul of the Jewish people is connected to the whole Torah.