Any ideas? Tenants' over-door hooks/hangers damaging jambs

[Ross Leavitt]

In our student rentals, probably 30% of the bedroom or bathroom doors and jambs have been damaged by tenants using towel/coat hangers that hook over the top of the doors. The hooks gouge the jambs and leave marks on the doors. Have other landlords had this problem? 

These are newer properties, and the doors and jambs are painted. We always repair the damage during turnover, but I'd like to figure out a way to stop it. Our student tenants don't always follow instructions. 

I'm thinking about permanently installing hooks on every bedroom and bathroom door, so the ones who want hooks won't have to use their own. Has anyone done this? Can you recommend a quality hook to use? If I installed one on every the bedroom and bathroom door, I would be installing about 400 hooks, so I don't want to use junk!