Saving Vault 68

[Stark]

I figured because the internal doors are all identical that there was nothing special about the door to the vault room (a room that, on the 101 pattern, seems custom-designed to prevent any heavy equipment moving in or out).

[CBG]

Staying in vault for the full 40 years is a recipe for disaster, either a in-vault-rebellion(s) kind of disaster, or bunch-of-old-men-in-wasteland disaster.
So, the first problem to be taken care of is the morale problem. The best solution is keeping existance of a woman in the vault a secret. Libido inhibitors added to water would be great, if available.
Next problem is opening the vault, 5-10 years after the vault closed. In that frame of time most of the en would still pretty young and able bodied, and chance of them getting crazy would not be too great. Destroying\hacking the lock would be the best idea. If not possible, limited destruction that would make repairing the door pretty fast would be needed. As all the vault doors we see in fallout 1 and 2 games have airlock-type layout with other ones behind them, the problem of destroyed main door could have it's consequences limited. Even better, a second door could be constructed (in safe conditions) in the middle of the airlock before opening the vault, making the airlock smaller, but letting the vault keep most of the ordinary security. If no airlock, then, well, build one inside the vault before opening the main door.
After the outside is accesible at will, i would send robots with radiation\chemical measuring equipment to check the conditions in area nearby the vault. If they are absolutely deadly, wait, check a few months later, repeat if necessary. When it gets a bit better, send well equipped gropus of few guys with protective gear, for searching the nearest vicinity of vault for survivors, useful junk, ,more protective gear (or materials for it) and information about the post nuclear world. Send more people to more distant areas as knowledge and experience in survival outside increase and conditions get better. This way people would not get bored enough to get stupid ideas like making a rebellion, and experience&stuff gained this way could be used to make an expedition to V69, if such trips do not end up getting at least a few dozens of women before.

[The Yosemite Bear]

dig tunnel between vault 68 and vault 69 (same experiment gender dispairity reversed)

[CBG]

This solution would be perfect if a vault had means for it. Digging many hundred kilometers tunnel without any heavy or specialized digging equipment and resources (tunnels need ventilation and support, huge tunnels need a lot of ventilation and supports), and trying to not get any contact with surface and it's contaminated atmosphere at the same time, would be something impossible. Even getting rid of the dirt\stone would be a problem without getting on the surface. Digging a spartan tunnel of 1m heigth, 1m width and 200 km length, would demand getting rid of 1m^2*200000m=200 000 m^3 of stuff to put somewhere. There are mines (with miners, lots of heavy, specialized mining equipment, no radiation above, and space for stone and dirt to store) that had less output in their whole operating history. And here we have guys that would have to use just hand tools, in a cramped tunnel, which would limit the amount of people working at the same time to a few. Even if it was just dirt, it would be 500000 tons of dirt to extract and get rid of. To do it in 20 years, it would be 34,2 tons a day. And notice, that, for example, when they reach 100 km mark, then they have to move these 34 tons of dirt\stone for a hundred kilometers through a little tunel, before they even can somehow get rid of it.
Under such conditions, even building a 2 km tunnel would be a huge undertaking. Just divide all the figures by 100, and they will still be pretty menacing.