2023 AMC 8
Complete problem set with solutions and individual problem pages
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 and represent a win or loss, respectively. For example, Lola won five matches and lost the fourth match. What was Tiyo's win-loss record?
- A.
- B.
- C.
- D.
- E.
Solution 1
We can calculate the total number of wins ('s) by seeing how many matches were players, which is matches played. Then, we can calculate the # of wins already on the table, which is , so there are wins left in the mystery player. Now, we will make the key observation that there is only wins ('s) per column as there are winners and losers in each round. Strategically looking through the columns counting the 's and putting our own 's when the column isn't already full yields .
Solution 2
We can look one by one. We see that Lola and Lolo won the first game and Tiya lost. This shows that Tiyo must have lost as well because the results must be wins and loses. We use the same logic for games and , giving us 's again. We look at the choices, and we see A is the only that starts with 's.
This shows our answer is
