Which area on the map was conquered by kublai khan?

He conquered the area marked with #3.

Explanation:

Kublai Khan, grandson of the great Genghis Khan set out to conquer the south of China and take over the area controlled by the Song Dynasty.  The task was not an easy one due to the conditions of the terrain and the Song's fortifications, but Khan's army was able to innovate new tactics and succeed in defeating the Song Dynasty around the year 1279.  Kublai Khan was the first to rule over all of China.

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