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a shotgun
the judge believed that it was futile to try and help pap
Pap bullied Judge Thatcher because he thought Judge Thatcher was keeping him from getting his hands on Huck's money. Pap believed that he had a right to take Huck's money for himself and was frustrated by Judge Thatcher's interference in his plans.
When the judge says pap could be reformed with a shotgun in "Huckleberry Finn," he means that pap's negative behavior might be permanently altered if he were to face a dramatic and extreme intervention, like being threatened or punished with a shotgun. The judge is pointing out pap's deeply ingrained flaws and suggesting that they may require a severe method to address.
the judge believed that it was futile to try and help pap
The new judge showed empathy and understanding towards Pap. He recognized Pap's struggles and tried to help him address the root causes of his behavior, rather than simply punishing him.
"sympathetic" or "lenient" would least describe the attitude of the new judge toward Pap in Huckleberry Finn, as the judge is portrayed as strict and unsympathetic towards Pap's actions and behavior.
Pap's personality could be anything. Since Pap could be a lot of person. Pap is quite a common nickname or name after all. He could be kind, timid, shy, clumsy, destructive, etc.
For money, so later he can get drunk with it.
Pap gains legal custody of Huck through a judge's decision due to being Huck's biological father. The court considers this as fulfilling the legal obligations and rights of a parent.
because he doesn't want to split father and son
to let Huck stay with his pap