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The staging area is located in the basement of Freddy Fear's. Upon arrival, Jen, Sergeant Radcliff, and Paige will be present. Talking to Paige, he will state that Penelope Hornwright has not yet arrived, having taken a detour to Hornwright HQ to make some last minute preparations.
Penelope will contact the team shortly, broadcasting to reveal that she was kidnapped by Hijack, and that the Raiders from the Crater demand that the Vault 76 dweller come to Hornwright HQ alone to talk terms of her release. Upon hearing the broadcast, Paige will realize the situation and give the player character a spare executive-level keycard given to him by Penny.
At the headquarters, the player character must enter the executive level through the elevator behind the reception at the ground floor, then pass through Daniel Hornwright's office to his private elevator and select the button leading all the way down to the Cave. Opening the door with the ID card will lead straight to the raider leader, Hijack. He will state in no uncertain terms that it is all or nothing; either Crater gets the gold or nobody gets it.
The player character can respond with Charisma 4+ to explain that everyone will benefit and give a peace offering, promising a share of the gold, then follow it up with Intelligence 8+ or Charisma 8+ to pacify him. Alternatively, two subsequent Strength checks (4+ and 8+) will intimidate him, or ask for terms. Exiting the conversation at any point will result in him getting angry and attacking, which will also complete the objective once he is killed.
Restoring the Motherlode
Once Hijack is dealt with, Penelope will be relieved, but concerned, as the raiders damaged the Motherlode upon arrival, destroying its navigation and decision-making modules. The player character can use Intelligence 8+ to propose reverse-engineering the payload system to deliver a refurbished core to the machine or just ask how to fix it.
Either way, Penelope will explain why the section of the headquarters building is named the Cave: To emulate the human brain's decision-making process, Hornwright decided not to invest in recreating the process, but replicating it. The Cave is a massive testing facility where human test subjects completed various mazes to provide the company with brain scans that were then used to construct an emulated neural network tailored specifically for mining.
To reconstruct the module, the player character has to complete the maze with Penelope offering feedback along the way. The way they deal with the fake walls will determine the Motherlode's future behavior (note that talking to the fake walls is a legitimate option and Penny will be exasperated by it). The maze is populated with mole miners, rad rats, and has a small amount of minor loot. At the end of the maze is the neural oscillator scanner, which has to be used to produce an intelligence module.
The final step is installing the module in the Motherlode back at the entrance to the Cave. Upon installing, it will retreat underground and the quest will complete.