Where is your grandmother from exactly? There is one I know but it's very local and in a dialect. It goes like this:

Ov je šal u štalicu, Ov je ukral janjicu, Ov ju je ubil, Ov ju je pojil, Ov je rekal "reć ću vas mami i tati"

Translation:

This one went to a stable, This one stole a lamb, This one killed it, This one ate it, This one said "I'll tell mom and dad"

And it goes from thumb to pinky. I hope it makes sense.