AMC8 2023 Problem 8

Lola, Lolo, Tiya, and Tiyo participated in a ping pong tournament. Each player competed against each of the other three players exactly twice. Shown below are the win-loss records for the players. The numbers '1' and '0' represent a win or loss, respectively. For example, Lola won five matches and lost the fourth match. What was Tiyo’s win-loss record?

\begin{array}{|c|c|} \hline \textbf{Player} & \textbf{Result} \\ \hline \text{Lola} & 111011 \\ \hline \text{Lolo} & 101010 \\ \hline \text{Tiya} & 010100 \\ \hline \text{Tiyo} & ? \\ \hline \end{array}

Answer Choices
A. 000101
B. 001001
C. 010000
D. 010101
E. 011000