The Meaning of Life, the Universe, and Everything.
The nation of Potatopia
28 days. I don't really have any major singleplayer survival worlds, so I went off of my house on my favorite SMP server. Fun fact: On said server, I actually have an enchanted instakill stick a friend gave me, but that wasn't one of the answers.
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If you ask me to click your dragons, I will click them until they are a pile of ashes.
25 days. Answered honestly. My house is almost always a hole in a shear cliff that you have to jump to reach or under a hill with the entrance underwater in a river bank, so I guess the mob proof front door counts for a fence? Raised entrances make for great grinders, because that's where all the monsters gather to try and reach you. With the cliff home just be careful when stabbing creepers right outside your front door or they could blow up your entrance, but you can knock them off the jumping block before they can blow and if you're high enough they'll take some fall damage. Alternatively you could always cage a cat near your door if you can get one.