How to solve rat riddle in Shido's palace?
Solution 1:
The map doesn't show all the vents right away but you have to locate them. (Similar you only see the locked door symbols once you try to open one.)
If you are stuck in any of the rat riddle stages, you have to scout the grey rooms for further vents, or flip the switch to activate the statues in other rooms.
In your particular case, the big grey room having all the enemies, there's another vent (cursor):
If one goes through there, one can unlock top doors, and from there one hit the switch and one is now able to unlock all the other doors on this level.