Modular Arithmetic




Dido's Problem



Smart Joe

Fuzzy Logic



At about the same time, I heard rumors that Smart Joe would be transferred to a different class after summer vacation. This worried me a lot because I wouldn't only be losing my best friend, but also the best math teacher I'd ever had. My begging for a watch became even more urgent. I wanted Smart Joe to teach me everything before he left.

Well, I didn't get my watch and nothing much changed until shortly before the summer break. At that time Smart Joe got faced with serious trouble. We had to solve problems like 14+4. Now on a watch which has only twelve hours, this is unsolvable. But Smart Joe didn't start using his fingers like our teacher always insisted on him to do. He had a much better and simpler idea. Having heard once that Europeans use twenty-four hours instead of am and pm, he just asked his parents to buy him a twenty-four hour watch.

Now, in contrary to me, Smart Joe had great folks, who telephoned some European friends right away and asked them to ship a twenty-four-hour watch by express mail. So only three days later, Smart Joe came to school with two watches, one to read the time on and one to do math problems on.

Now Smart Joe could not only add four to fourteen, which equals eighteen (as you can check for yourself), but also big numbers like ten plus twenty-one, which equals seven.


Solve these problems using Smart Joe's twenty-four-hour watch:


Sadly enough the rumors were true and the goodbye on the last day of school was the goodbye for ever. I must have been pretty gloomy at home, because my parents decided to buy me a watch to cheer me up. I eagerly opened the present wondering if it would be a twelve or twenty-four hour watch. It was neither! It was a digital watch!

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