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I heard someone say that mobs stop moving even though they are still loaded, if you get too far away from them. Does anyone know how many levels I can build. I have a 23 block drop, and each level are 3 blocks tall including the floor.

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At certain distance - over 32 blocks - mobs stop wandering randomly. They will still pathfind to iron golems, zombies will keep chasing the player, endermen damaged by rain will teleport, but in general mobs will stand still unless they have an explicit reason not to.

Even within the 32 block radius mobs wander only rarely, so definitely build a design where they are pushed (e.g. by flowing water) instead of depending on them falling into holes/streams/etc all on their own - efficiency of the latter is abysmally bad.

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You should be able to use the whole height because Minecraft chunks are 16x256x16. The height of a chunk is all one chunk.

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