Slime Statues are large stone statues which resemble Slimes. Two types of those exist: normal ones which are used as decorations around the Far, Far Range and the others, who have in their mouths a hole carved in where you can put a Plort in, which are used for puzzles. There are three examples of these puzzles, located at the entrance to The Ruins which requires various plorts from different Slimes, the teleporter to The Glass Desert, which requires a couple Quantum Plorts, and at four different fountains within the Glass Desert itself, each of which require plorts from various Slimes found within the desert.
The Moss Blanket
Rock Statue
You can find the Rock Statue next to the door that leads to The Indigo Quarry in the Ruins Entrance.
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Tabby Statue
You can find the Tabby Statue next The Ruins Gate on top of a platform in the Ruins Entrance.
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Phosphor Statue
You can find the Phosphor Statue on top of a normal statue next to a pillar in the Ruins Entrance.
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Rad Statue
You can find the Rad Statue on top of a destroyed wall next to the pillars in the Ruins Entrance.