(First floor.) Ration of Food blocks the door. Mage pretty much starts with everything you need to solve that room.
Edit: This seed is crazy, already with artifact and wand on the first three floors. LBX-MZH-SYDv2.5.2 (Mage; On Diet&Faith Is My Armor&Forbidden Runes)
It’s just about the starting items: Staff of Magic Missile, Cloth Armor, Ration of Food and 0/20 waterskin.
Only the food ration will be unavailable, but the sheep are long gone when you get hungry. Also throwing waterskin wouldn’t be an issue, but you’ll have to wait with collecting dews.
I guess. It’s just such a miniscule thing to be pleased with. You can throw anything you find on floor 1 at those traps to trigger them except a potion.