Which of the following was a problem faced by the average Chinese citizen during the Song dynasty?

a.the shrinking use of the civil service exam and thus the lack of opportunity to obtain a government position
b.the control of the Chinese treasury by northern invaders led to greater taxation
c.an influx of Christian missionaries countering Confucianism
d.overcrowding and health concerns in urban centers
e.greater acceptence of foreigners leading to an erosion of Chinese identity

To determine the problem faced by the average Chinese citizen during the Song dynasty, let's analyze each option:

a. The shrinking use of the civil service exam and lack of opportunity to obtain a government position: The civil service exam was an important means of obtaining a government position during the Song dynasty. If the use of this exam was shrinking, it could limit the opportunities for the average Chinese citizen to secure a position in the government. This could be a potential problem.

b. The control of the Chinese treasury by northern invaders leading to greater taxation: This option suggests that northern invaders had control over the Chinese treasury, which resulted in increased taxation. If true, this could cause financial burdens for the average citizen, making it a problem.

c. An influx of Christian missionaries countering Confucianism: This option implies that an influx of Christian missionaries was countering Confucianism, the dominant belief system in China during the Song dynasty. While this might have cultural implications, it may not necessarily be classified as a problem faced by the average citizen.

d. Overcrowding and health concerns in urban centers: Overcrowding and health concerns in urban centers can be common problems in any society. If the Song dynasty faced these issues due to population growth, it can be considered a problem faced by the average Chinese citizen.

e. Greater acceptance of foreigners leading to an erosion of Chinese identity: This option suggests that greater acceptance of foreigners resulted in an erosion of Chinese identity. While this might have cultural implications, its direct impact on the average Chinese citizen is not clearly stated.

Upon analyzing the options, it seems that options a, b, and d are more directly related to problems faced by the average Chinese citizen during the Song dynasty. Therefore, the most likely answer would be a combination of a, b, and d.