Admit it: You're dumb and lazy.

Brace yourself. This is yet another of my trademark puzzles. There's no prize for this one, but at the same time, I will never confirm if your answer is correct. However, if you need the answer with haphazard diagrams and minimum explanations poorly demonstrating the logic, I'll sell you the answer for 50 USD through paypal. I am not shitting you. I want money for smokes.

glhf

gg

*~*~*~*~*~*~*~*~*~*~*

The Villa with 14 Doors

A sadistic, self-loathing, and openly misanthropic prick named Kelvin finds an old abandoned villa. It’s not dilapidated nor show any sense of collapsing, but it reminds Kelvin of those haunted houses where horny teenagers have sex and imagine serial killers chopping them up for the sexual thrill. Suspicious of the place, he walks around it to take note of any peculiarities (you know, to see if it was just another thieve's hideout, underground drug lab or worse--horny teenagers procreating. Did I mention he hates teenagers and believes they should never reproduce their stupid?). After circling around the perimeter and peeking through the windows, he learned three things about the place:

• The villa is completely empty, or at least it appears that way after peaking through the windows.
• Excluding the surrounded courtyards and gardens, the villa building itself is in the shape of a one story cube.
• There are 3 windows, one on each side of the walls with the exception of the fourth side having the entrance-way which has the only door leading inward or outward. The windows are always in the center of the wall.

• In any given room, two or more numbered doors leading in/out of that room will never lead to the same room.
• There will always be a door between two rooms if they share the same wall.

He enters door “1” and sees doors “3”, “4”, and “6”. He also sees a window. He checks himself out in the reflection in the glass. He may be self-loathing, but he’s also narcissistic.

He goes back to the entrance-way and this time enters door “2” this time. He sees the doors “3”, “8”, and “12” but this time, no window. Is his mind playing tricks with him?

He returns to the entrance-way (because he was confused as fuck) and sees something whittled into the walls below the plaque. Someone in the past also trespassed into the abandoned villa and explored the place. It says ‘’there are 14 doors in total and all the rooms with a window has all of its doors add up to a multiple of 14. Cool!”.

To check this statement, he goes through the “2” door, then takes the “8” door and finds two additional doors marked “9” and “11”. He’s relieved that he finds a window this time. He checks himself out again.

Bored and unamused as fuck (there’s only so much time Kelvin can waste checking out his own reflection), the prick keeps opening doors and finds the villa completely empty with the except of spiders, dust, and display cases of whatever. It’s not worth looting and carrying all the way city so he can pawn them for smokes.

He is getting bored of the place, but at least he can leave once the rain passes. While waiting, he explores the house and finds out that assuming that light passing through windows can illuminate the entire room, no light can pass through the roof and if all the doors are shut tightly, then there are several doors that never see the light of day.

Question:

If you add up the numbers on these specific doors, what would be the sum of all the “lightless” doors?

Bonus question:

Assuming that all the doors of the villa are closed, what is the minimum number of doors needed to be opened to access every room?