Yeh-Lu Ch'u-Ts'ai is the Chinese minister who muted some of Ogedei's more rapacious instincts.

Explanation:
Ogedei Khan was the third son of Genghis Khan and the second Great Khan of the Mongol Empire. During his reign, he expanded the empire and was known for his aggressive and often ruthless military campaigns. However, Ogedei's rapacious instincts were sometimes curbed by the influence of his ministers, one of whom was Yeh-Lu Ch'u-Ts'ai.

1. Who is Yeh-Lu Ch'u-Ts'ai?
Yeh-Lu Ch'u-Ts'ai was a prominent Chinese statesman and a trusted advisor to Ogedei Khan. He served as the Minister of Finance and was responsible for managing the empire's finances and economic policies. Yeh-Lu Ch'u-Ts'ai was known for his administrative skills and his ability to temper Ogedei's more aggressive tendencies.

2. How did Yeh-Lu Ch'u-Ts'ai mute Ogedei's rapacious instincts?
Yeh-Lu Ch'u-Ts'ai's role as a minister was crucial in curbing Ogedei's rapacious instincts. He advocated for policies that promoted stability and economic prosperity within the empire. He emphasized the importance of trade and commerce, encouraging the expansion of the Silk Road and establishing diplomatic relations with neighboring kingdoms and empires.

Yeh-Lu Ch'u-Ts'ai also played a significant role in managing the empire's finances. He implemented policies to ensure fair taxation and efficient collection of revenue, which helped finance Ogedei's military campaigns without excessively burdening the population. By maintaining a stable economy and preventing excessive exploitation of conquered territories, Yeh-Lu Ch'u-Ts'ai effectively muted Ogedei's more rapacious instincts.

3. Impact of Yeh-Lu Ch'u-Ts'ai's influence
Yeh-Lu Ch'u-Ts'ai's influence on Ogedei's reign had a significant impact on the Mongol Empire. His emphasis on stability and economic prosperity helped consolidate the empire's control over vast territories and fostered positive relationships with neighboring states. By curbing Ogedei's rapacious instincts, Yeh-Lu Ch'u-Ts'ai contributed to the longevity and stability of the Mongol Empire.

In conclusion, Yeh-Lu Ch'u-Ts'ai, as the Chinese minister, played a crucial role in muting some of Ogedei's more rapacious instincts by implementing policies that focused on stability, economic prosperity, and fair governance. His influence helped ensure the longevity and success of the Mongol Empire during Ogedei's reign.