Irina asked five of her students how many of the five of them had studied the day before. Pol said none, Berta said only one, Ona said exactly two, Eugeni said exactly three and Gerard said exactly four. Irina knew that those students who had not studied were not telling the truth, but those who had studied were telling the truth. How many of these students had studied the day before?
I'd say one.
100000000000000000000000000
Let's analyze the statements made by each student:
1. Pol said none. This means that Pol did not study.
2. Berta said only one. This means that Berta studied.
3. Ona said exactly two. This means that Ona did not study since she stated that exactly two students studied.
4. Eugeni said exactly three. This means that Eugeni studied since he stated that exactly three students studied.
5. Gerard said exactly four. This means that Gerard did not study since he stated that exactly four students studied.
From the statements, we can deduce that Pol and Gerard did not study, and Berta and Eugeni did study.
Therefore, a total of two students had studied the day before.
To solve this problem, we need to analyze each student's statement and determine how many of them had actually studied the day before.
1. Pol said none: This means Pol did not study. Since Pol is not telling the truth, we can conclude that at least one student studied.
2. Berta said only one: If Berta is telling the truth, then only one student studied. However, since Pol's statement was false, Berta must be lying as well. Thus, Berta did not study.
3. Ona said exactly two: If Ona is telling the truth, then two students studied. Since both Pol and Berta did not study, and Pol's statement was false, we can conclude that Ona is lying. Therefore, Ona did not study.
4. Eugeni said exactly three: If Eugeni is telling the truth, then three students studied. Since Pol, Berta, and Ona did not study, and their statements were false, we can conclude that Eugeni is lying. Therefore, Eugeni did not study.
5. Gerard said exactly four: If Gerard is telling the truth, then four students studied. Since we have already determined that Pol, Berta, Ona, and Eugeni did not study, and their statements were false, we can conclude that Gerard is lying. Therefore, Gerard did not study.
Based on our analysis, none of the students' statements are true. Therefore, none of the students studied the day before.