How many tribes were in the Northern Kingdom of Israel?

There were originally twelve tribes in Israel, the sons and grandsons of Jacob. In 930 BC, ten tribes formed the independent Kingdom of Israel in the North (Asher, Dan, Ephraim, Gad, Issachar, Manasseh, Naphtali, Reuben, Simeon and Zebulun). Judah and Benjamin made up the Kingdom of Judah in the South.

Of the original 12 tribes of Israel (sons of Jacob) who took Canaan, 10 tribes made up the Northern Kingdom - Asher, Dan, Ephraim, Gad, Issachar, Manasseh, Naphtali, Reuben, Simeon, and Zebulun. The tribes of Benjamin and Judah established the Kingdom of Judah in the south. The northern tribes were eventually assimilated, and are known as the 10 Lost Tribes.

This has long been a puzzle for me. Simeon's territory was within the borders of Judah. How then was Simeon a part of the northern kingdom?