The Prophet of Allah, sallallaahu ‘alayhi wa sallam, affirmed their ingenious deductions

Hanash ibn Al-Mu`tamir (a Follower; belonging to the generation following the Companions) reported that `Ali was in Yemen, they dug a hole

trying to hunt a lion, and the lion fell in it. When they were overlookingthe hole and crowding it, someone fell in. That person grabbed someoneelse, and that person grabbed someone else, and so on, until four peoplefell in the hole, and the lion wounded them while they were in there. Oneof them took a spear and killed the lion, and all of them died from theirwounds. They differed over it so much so that they wanted to fight oneanother over it.

Ali went to them and said: “Are you looking to fight, while the Messengerof Allah, sallallaahu ‘alayhi wa sallam, is alive? I will judge between you, and ifyou agree, then that is the judgment, and if not, stop disputing with one anotheruntil you can go to the Prophet of Allah, sallallaahu ‘alayhi wa sallam, and hecan judge between you. Anyone who commits aggression after that will have noright. From the tribes that dug the hole, collect a fourth of the Diyah [blood money], a third of the Diyah, a half the Diyah and the entire Diyah.” 

So he judged that the [rightful inheritors of the] first man should get aquarter of the Diyyah, the second a third of the Diyyah, the third a half ofthe Diyyah and the fourth the entire Diyyah. Some of them were pleased(with this judgment) while others rejected it. They took their dispute tothe Prophet of Allah, sallallaahu ‘alayhi wa sallam. When they went to theProphet of Allah, sallallaahu ‘alayhi wa sallam, they found him next to Maqaam (the station of) Ibraaheem (next to the Ka’bah) and told him wha thappened. He, sallallaahu ‘alayhi wa sallam, said: “I will judge between you,” and sat down with his hands held around his knees. A man from them said: “Ali judged between us,” and they told him the story. The Messenger ofAllah approved Ali’s judgment.1This is because the four men who were killed by mistake when the people crowded around the hole (to look at the lion) deserve the Diyah for being killed by mistak from those who were present. The first person who was killed, was killed because he was pushed down (and stepped on), but he caused the death of three others by pulling them down with him. He deserves the Diyah for being killed by mistake, but owes three
fourth of the Diyyah for the three whose death he caused. The second man deserves a third of the Diyyah but owes two thirds of the Diyah for the two whose death he caused. The third man deserves a half of the Diyah and owes a half because he caused the death of one man by pulling him down with him [so each of the three men pulled one man down with him, the first caused three men to die, the second two men and the third one man]. The fourth person deserves the entire Diyah because he did not cause the death of anyone.

The Prophet of Allah, sallallaahu ‘alayhi wa sallam, paid close attention to his cousin, `Abdullaah ibn `Abbaas, because he witnessed
that he had attributes showing his distinction and intelligence.

In another narration, the Messenger of Allah, sallallaahu ‘alayhi wa sallam, was at the house of Maymoonah (the wife of the Prophet of Allah, sallallaahu ‘alayhi wa sallam) and Ibn ‘Abbaas put some water for him to use as ablution at night, and Maymoonah said: “O Messenger of Allah, `Abdullah ibn `Abbaas has placed this for you here.” He, sallallaahu ‘alayhi wa sallam, said: “O Allah, give him understanding in the religion, and teach him the interpretation of the Quran.”Ibn `Abbaas was one most famous exegetes of the Quran among the Companions, even though he was one of the youngest Companions. Hewas born three years before the Prophet of Allah, sallallaahu ‘alayhi wa sallam, migrated to Madinah, and he accompanied the Messenger of Allah, 

sallallaahu ‘alayhi wa sallam, from a very young age. This is because he was closely related to the Messenger of Allah, sallallaahu ‘alayhi wa sallam, and
his wife Maymoonah.
The Messenger of Allah, sallallaahu ‘alayhi wa sallam, died when Ibn
`Abbaas was thirteen years old.
His intelligence was manifest and the Commander of the Believers,
`Umar knew that, so he would keep him close to him