Project Management sheet - advanced list problem (Repost)

Hi. Please see the attached file. I have this sheet where I have different projects. Then I have created a "Name_database" sheet. Each person can be allocated to a project, but only one project. When you have chosen one person, he/she is out of the list.

But one person can actually be allocated to more than one project - if the start date and end date does not overlap. But how do I implement that?

All suggestions are welcome.

I have reposted this problem here in the VBA section, just to see if there is anyone who might have another suggestion to solve it.

Original post

Pl see the attached file.

@Patel45: I always google stuff before I am posting something in this forum. Not all of them are free and they can do a lot of fancy things, that I actually don't need - that was why I tried to post my problem here.
@kvsrinivasamurthy: Thanks for your constribution, but it seems to have an error. I can pick Nina for both project 3 and 4

I think I got it...

File replaced in last post with latest revision.

Pl see attached file. Formulas are changed.

@jhren: What should the "list" reference be?
@kvsrinivasamurthy: Seems to be working! I'll test it igen later today! I can't thank you enough.

@Jhren: Sorry for my late reply! But yeah, exactly, the data validation reference. Sorry for my unclear information .

As stated in my EDIT, I just directly selected the range for each set of data validations. You can name the range if you want...