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After witnessing a discouraging duel Joel goes to the office and stops by Exton and Florence, the office clerks. Florence is annoying Exton who is working when they start talking about how principal York was informed that Nalizar would duel with Fitch. Joel spilled the news that Nalizar was victorious and took Fitch's place. There is hope that in a year Fitch can overcome Nalizar and meanwhile teach Joel.
Joel was bored to death in his math class because he knew everything. Professor Layton had discovered that Joel didn't do his homework, and after class he told Joel that because he had done only 9/40 assignments , he had to take summer tutelage for geometry. Layton was suspicious that Joel was cheating and when he immediately started completing his assignments in seconds he was assured.Joel was saved when he pointed out a mistake in Layton's drawing which impressed him. Joel didn't have to do tutelage and was told by Layton that Joel should've been a rithmatist.
=== Chapter 3 ===
After history class Joel has to do math. Joel likes mathematics as for geometry is the base for [[Rithmatics]]. The [[Armedius_Academy#Rithmatic_Campus|Rithmatic campus]] was set apart to the [[Armedius_Academy#General_Campus|General campus]] though -- as in Joel's math class -- some of the Rithmatists had to join the ordinary classes because of lacking the basics.
When Professor [[Layton]] comes to check off last night's assignment, Joel is caught in not having done them. When Professor Layton dismisses the class he tells Joel to stay. Though Joel got perfect marks in the tests, Professor Layton isn't convinced about Joel's knowledge and Joel realizes that the professor thought him cheating. Joel supposes to do the assignment in these last few minutes of the class and begins to do. The professor thought somebody told Joel the answers and draws a new task on the board. Joel solves it quite instantly and points out that the drawings where not really accurate. He proves to be able to draw perfect lines and circles by eye and convinces Professor Layton that he already knew what was taught during this term, and also trigonometry and algebra. Finally the professor gives Joel the pass for geometry class.
=== Chapter 4 ===
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