Final answer:
Austria-Hungary faced the greatest challenge remaining unified with a large variety of ethnic groups seeking independence within its borders in the late 1800s.
Step-by-step explanation:
In the late 1800s, Austria-Hungary faced the greatest challenge remaining unified with a large variety of ethnic groups seeking independence within its borders. This was due to the presence of several different ethnic groups, such as the Czechs, Slovaks, Poles, and Ukrainians, who desired their own independent states.
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