Halakhah к Берешит 18:28

There is a well-known controversy with regard to whether a minyan consists of ten individuals upon whom public prayer is obligatory, or whether it may be formed by nine adults together with one minor. According to the commentary of Rosh on Berakhot 48a, it would appear that the authorities who permit the inclusion of a minor maintain that in actuality it is the Divine Presence which is included as the tenth member of the minyan.¹²See, however, Ba‘al ha-Ma’or, Berakhot 48a. Attention may be drawn to the biblical narrative concerning Abraham's supplication on behalf of Sodom and Gomorrah. Abraham at first prayed that those cities be spared if fifty righteous inhabitants were found. Rashi explains that in actuality five cities were marked for destruction and Abraham prayed that the cities be spared if ten righteous persons—a minyan—could be found in each. Subsequently Abraham prayed that the cities be spared even in the event that only forty-five righteous persons could be found. Rashi (Gen. 18:28) comments that Abraham recognized that a minyan must be found for each city, but beseeched the Almighty that He include Himself in that number. This would explain why those authorities who sanction the inclusion of a minor as the tenth person require that he hold a written scroll of one of the books of the Pentateuch in his hand. In reality it is the Divine Presence which is symbolized by the scroll of the Law which is included. The presence of a minor is required by virtue of the rabbinic decree which regards him as being already a quasi-member of the minyan because the minor will one day share the religious obligations of the rest of the minyan.