Question : Share folder is giving read only messages and users can't save

Suddenly the shared folder on the file server is giving users the message that a file already exists with the name they are trying to save. Do they want to replace it?  Then when they click yes, it says that the sharedfolder\foldername is read only. There appears a file with the name they want to save with no kb, an empty file.
The shared folder says read only with the correct share permissions and NTFS permissions assigned accordly.
I have click on the read-only attribute to take it off and it proceeds to do that to all the folders and files in the share.  But when I click on properties it still says read-only and the users still can't save to the folder.
It is strange because not all folders are effected. One or two folders can still be saved to.
Everyone is panicing.  They can still save to their my documents folders on the server, just not this shared folder that students use for class projects.
Really need some ideas
.After I posted, I realized that you may need more info to help me.  Sorry, I'm pretty stressed.
File structure: Volume\shared data folder\Class Project folder\folder for students to save class assign.= The whole Class Projects folder is read-only.
Volume\shared data folder\Students$ =all student home folders-no problems saving here not read-only
Volume\shared data folder\Teachers$ =all teacher home folders-no problems saving here-not read-only
And an interesting thing happens, when a teacher tries to save to the Class Projects folder, they get the same thing happening with the file name exists, then a file with 0kb.. But I just got this error message: The save failed due to out of memory or disk space (volumeletter\foldername\filename).  The disk is full. Free some space on the drive or save to another location.
I checked the Volume in MY computer:  capacity=169 GB, used=46.7, free space=122GB.  In computer management: virtual disk one (which has the volume) shows the same thing.  The user that I tried was not over the disk quota.
All of these shares existed when I got here. I have only added folders to the Class Projects folders for teachers so their student could save on-going and group projects in. Some folders work and some don't.
in each category, old ones and new ones.
I have no idea what is going on.?!

Answer : Share folder is giving read only messages and users can't save

The Share Permissions look good but the NTFS permissions can be set to Modify. Only people I ever give full control to NTFS Permissions is IT and Managers. If the students make the file/folders hidden you will still be able to see them.