Daily Math Puzzle: 2026-07-20

Carol — There are 4 players, and each played every other player exactly once, resulting in 6 total matches. Since a win earns 1 point and a loss 0 points, the total points distributed among all players must equal the total number of matches, which is 6 points. The given scores (Alice 3, Ben 0, Carol 1, David 2) sum to 3 + 0 + 1 + 2 = 6 points, confirming the scores are consistent. Now, let's analyze Ben's score. Ben has 0 points. This means Ben lost all 3 of his matches. Ben played against Alice, Carol, and David. Since Ben lost all his matches, he must have lost to Carol. Therefore, Carol won the match against Ben. To verify, we can reconstruct the full tournament outcomes: 1. **Ben (0 points)** lost to everyone: Alice, Carol, and David. (A>B, C>B, D>B) 2. **Alice (3 points)** won all her matches. Since she played 3 matches, she must have beaten Ben, Carol, and David. (A>B, A>C, A>D). This is consistent with Ben's losses. 3. **David (2 points)** won 2 matches and lost 1. We know David beat Ben (from Ben's score) and David lost to Alice (from Alice's score). So David's second win must have been against Carol. (D>B, D>C, A>D). 4. **Carol (1 point)** won 1 match and lost 2. We know Carol lost to Alice (from Alice's score) and lost to David (from David's score). Her only win must have been against Ben (which we deduced earlier). (C>B, A>C, D>C). All scores are consistent with this reconstruction, and it uniquely confirms that Carol won the match against Ben.