2023 AMC 8 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?

\textbf{(A)} 000101 \qquad \textbf{(B)} 001001 \qquad \textbf{(C)} 010000 \qquad \textbf{(D)} 010101 \qquad \textbf{(E)} 011000

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.