in three generations,
granny has three children
girl1, boy, girl2
girl2's older child (a boy) has the same birthday as girl1, the oldest child in her generation
and boy's youngest child (in a family with the same pattern as his own: girl, boy, girl) has the same birthday as girl2, i.e. the last child in a family with the identical pattern.
From granny's perspective: her oldest child has the same birthday as her oldest grandchild, and her youngest child has the same birthday as her youngest grandchild (of seven), in a family with the same pattern as her own.