Hostile mobs spawn inside interiors despite high lighting levels.

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We're tracking this issue in MCPE-302, so this ticket is being resolved and linked as a duplicate.

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Can you provide a picture, video, or world save to show the area where monsters spawn unexpectedly?

Yeah, the same thing happened to me. I keep the area around my house well lit. Mobs never spaw around my house. But after the nether update hostile mobs keep spawning even at high light levels. A creeper even spawned inside my house.

I tried to take a picture this time when a skeleton spawned inside my house but I was at low health so there was nothing I could do.

Just put a sign on the block where it spawned and send a pic of the room.

There are two scroll bars so that you can look around the image. The arrows are where the skeleton was. I put signs for where each mob was at the time of the encounter. I first experienced it right after the nether update. I was excited for the new biomes so I went to the nether and when I came back it was dark. Usually, there are no mobs when I come back because the area around my house lit up. But when I came back there were hostile mobs everywhere. Worse when I entered the house a creeper spawned. I carefully lured it outside the house and killed it. The next day I went back to the nether I came back. This time it was light outside. But when I went in the house a skeleton was inside. I can't tell if it happened because I went to the nether or if it was because of something else.

I think you are just experiencing the new despawning behavior in 1.16 that allows new mobs to spawn more frequently.

Monsters spawn below light level 8. The spot where you have the creeper sign is at 8 counting from the torch above the bed, and there are clearly darker spots further into the room. So, I think your room is not well lit enough to block monster spawns. It probably was safe in earlier versions because there were monsters hidden in nearby caves that were filling the cave cap. Now they can despawn regularly and allow new spawns.

Thank you for your report!
We're tracking this issue as MCPE-302, so this ticket is being resolved and linked as a duplicate.

That ticket has already been resolved as working as intended, which means this is not considered a bug and won't be fixed. Please do not leave a comment on the linked ticket.

As GoldenHelmet mentioned, mobs spawn in light level 7 and below. Given the size of the room the lighting you have (3 blocks up on the wall around the edges) is not sufficient. New mob despawn mechanics mean that hostile mobs spawn more readily which is likely why you've not had this issue prior.

If you haven't already, you might like to make use of the search feature to see if the issue has already been reported.

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Thanks a lot for the help. I'll check and make sure I put more torches up in the room and I'll update you if the issue persists.

You could also put carpet on the floor the middle of the room to block spawns, put jack-o-lanterns in the floor or ceiling, make a glass skylight, attach lanterns to the ceiling—there’s lots of options!