A great way to keep a baby reaper fed (at least until it becomes juvenile) is by waiting until it has 30 minutes left, then filling your inventory as much as possible with cooked meat. Wait until the reaper burst out, claim it, then let it eat you and your corpse. After that the reaper should get all your inventory, so it should be filled with cooked meat and keep it fed. And in the mean time, place a trough by its pen and fill that with cooked meat.

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