If users are unable to save files due to permissions on their home directories, what is the most probable resolution?

When users are unable to save files in their home directories, it typically indicates a permissions issue. In Unix-like operating systems, permissions control who can read, write, or execute files and directories. The "w" permission specifically refers to the ability to write to a file or directory. By adding the "w" permission for the users, you grant them the ability to create and modify files within their home directory, which is directly related to the issue described.

The other options would not effectively resolve the problem. Adding "x" permission for the group might allow users to access the directory but would not necessarily enable them to write files there. Similarly, removing "x" permission for others or removing "r" permission for the group could restrict access and could complicate collaboration, but they do not directly solve the issue of writing files if users lack write permissions. Thus, the most effective and relevant action to resolve the problem is to add the write permission for the users.