Here's the matching of the problems to their corresponding solutions:
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# of national representatives to have - Great Compromise
This compromise established a bicameral legislature with the House of Representatives based on population and the Senate with equal representation for each state. -
how to elect the president - Electoral College
This system was established to create a mechanism for electing the president, balancing the influence of populous states with that of smaller states. -
population numbers for slave states - Three-Fifths Compromise
This compromise determined that slaves would be counted as three-fifths of a person for the purposes of representation and taxation, thereby affecting the population counts for the purpose of representation. -
protect citizens from an abuse of government powers - Bill of Rights
The Bill of Rights was introduced to ensure individual liberties and to protect citizens from potential government overreach and abuse of power.