What does it mean when a married Indian girl shares her number (not fake) during a random approach?

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In my experience, there are two reasons why ‘taken’ women do not beat you over the head with their relationship status the very first time you talk to them. The first is that they’re interested in you and don’t want you to deal with them “as a married woman.”

The second is that they’ve internalized the idea that “guys won’t talk to you if they know you’re taken,” bit. They’re probably not interested in you other than socially, they’re just being polite.

You need to find out which it is before you can proceed. I suggest you do so sooner rather than later.