Strength in Numbers

Strength in Numbers is a main quest in the Fallout 76 update Wastelanders.

Background
After the Vault Dweller has dealt with the Free Radicals, Duchess needs the residents' help to find her missing guards. It is up to the residents of Vault 76 to find them, if they're still alive.

Find Duchess' people
After speaking to Duchess, tune in to the Transmitter Signal radio station. A map marker will then be placed on Gauley Mine. Near the mine's exit will be the scene of a battle, with Scorched corpses and ash piles scattered around what looks to be an Assaultron arm, indicating that some of the Scorched were disintegrated by an Assaultron's head laser. Upon searching the Scorched corpses for clues, one of them will have the Gauley Mine production log on their body, read it to continue the quest. Alternatively, the player character may enter Gauley Mine after receiving the transmitter signal to locate Sol and Polly in any order, thereby skipping the investigation part of the quest.

Head inside the mine through the entrance, and be ready to fight leveled Scorched appropriate to the player character's level. Upon entering the mine and past the second bend, at the tunnel entrance will be a wounded man, speak to him. The player character has the option to give Sol a stimpak, or to lie to him that they can't help him. After talking to Sol, he will start to make his way back to the Wayward. With one guard found alive, next is to find the other missing guard. Continue deeper into the mine, until one reaches the mine's end with a large cavern room with water, and an overturned mine cart with a robot head on top. The robot head will yell at the player character to come closer, wishing to speak to them. Speak to the Assaultron head. Polly will suggest that the player character use her head laser to wipe out the Scorched. Polly's head will then auto-equip as a weapon. Three waves of Scorched will arrive, and must be defeated to progress. With fifty worn fusion cells, use Polly's head to defeat the Scorched. A boss type Scorched foreman will arrive in the last wave. Defeat all remaining Scorched in the room to continue. Exit Gauley Mine either through the nearby exit, or through the front entrance, and return to the Wayward inn. Once outside the mine, take note that the worn fusion cells Polly's head uses will corrode, depleting all ammunition for the quest weapon.

Alternatively, the player character may speak to Polly first near the exit, rescue her from the Scorched, and speak to Sol afterwards in Gauley Mine. Speaking to both guards is required to complete the quest. Carrying Polly's head will result in some dialogue when speaking to Sol for the first time.

Once back at the Wayward, equip Polly's Assaultron head in the Pip-Boy, or draw it if already equipped. Polly will need a temporary replacement for a body, place her head on the moonshine jug on the bar counter. Duchess and Polly will then ask and plead the player character to help them find a new body for Polly, with Sol knowing where to find a new pristine Assaultron body. The player character will have to accept the crew's request to continue the quest. Speak to Duchess to accept. Duchess will then give Sol's transmitter and Sol will also give the Duncan & Duncan entrance card to the player character.

Find a new body for Polly
After speaking to Duchess and accepting the new objective, travel to Summersville along the main road towards the end of town, and enter Duncan & Duncan Robotics through the green door which is hardly blocked. Blood Eagles inhabit the town now, and may attempt to stop the player character if they are detected. Once inside the Duncan & Duncan Robotics building, speak to Skinner at the front desk. Skinner will mention the pristine robots on display are all spoken for, the player character will need to convince Skinner to let them access the showrooms. This is possible through persuasion or at the price of buying an access card:
 * If the player character has achieved the rank of General in the Whitespring bunker, a new dialogue option appears to bypass the need to buy an access card or sneak through the showrooms, allowing easy access to the Assaultron showroom. Whereas regardless laser grids surround the pristine robot models among laser turrets. Skinner may yell at the player character that the showrooms are for paying customers only, but he won't stop the player character.
 * If the player character has graduated from Camp McClintock, there is a dialog option to claim a robot body in the name of the US Military. Skinner then hands out a pass card for the upstairs showroom.

Select a pristine robot body to interact with. The choices are a protectron, a Mr. Handy, or an Assaultron body. The player character may need to sneak around the showrooms as to not trigger the laser grids, or to alert the laser turrets, and to open the Picklock locked doors to navigate the area easier.
 * Climbing up to the attic through a hole in the Mr. Handy Showroom wall, will allow the player to find an apologetic note, mentioning an address, and a holotape of the ranting of the mad former proprietor, who mentions his brother set the passcode to a certain address. This number (88888) can be used on the keypad to access the Assaultron Showroom.
 * A small hallway behind the Assaultron body is available to safely plant the transmitter signal through a hole in the back wall, without needing to enter combat.
 * One may also just pick the lock to the Assaultron Showroom, though it requires Picklock level 3.

Once a pristine robot body has been selected, return to the Wayward once more. Polly will want to know what kind of body she has to look forward to, as will Duchess. When the player character arrives at the Wayward inn, speak to Polly. Tell her the good or bad news about her new body. Duchess will then remark it's time to talk about Crane.

Talk to Duchess
Speak to Duchess again, she will ask that the player character follows her upstairs. Sol will be at the top of the stairs, apparently minding his own business. The quest will complete once Duchess walks upstairs, follow her to learn the truth about Crane.