I request a hint, clarification (if needed), or your approval (if my doutful solution is correct) for this problem:
Problem 11. A teacher drew several circles on a sheet of paper. Then he asked a student "How many circles are there?" "Seven," was the answer. "Correct! So, how many circles are there?" the teacher asked another student. "Five," answered the student. "Absolutely right!" replied the teacher. How many circles were really drawn on the sheet?
Every hint or clarification you propose is really acknowledged. Here's the link of the book in case you need it.
Here's my doubtful solution:
https://i.stack.imgur.com/hCNMV.png
My solution contemplated an additional square. So if we count only complete circles, there are 5 circles in total; but, if we count half circles, we obtain 4. If we join them, we obtain 2 new circles. So there are 7 circles in total.
Thank you very much!
P.S. You may note that the book has a section of answers and hints. However, I eagerly wish to discuss the problem, and solve it (being given your approval) without seeing the answer. Without seeing the answer and receiveing feedback, I own the possibility of re-thinking my answer, refining it, and improving my mathematical thinking. This is by far the most important exercise for me.
P.S.S. I am not an English-native speaker, so every correction to my writing is really appreciated!
The teacher was not standing at one of the extreme ends of the classroom. That is, the teacher had a few students to his left, and a few to his right.