The Marvelous Math Club Reply

There are over twenty clubs currently functioning in BSGE. Students, based on their hobbies, can choose to attend clubs with themes such as French, Yoga, Fashion, Math and many others. For me, as an addict to Sudoku-like puzzle and logic games, Math Club was an obvious choice. Hence, as soon as Middle school Math Club opened, with Mr. Mehan at its helm, I was on board, along with 50 other Math enthusiasts. The club offers engaging and challenging mathematical activities that can build skills and logical thinking.

Every Wednesday from 2:15 P.M. to 3:15 P.M. Middle School Math Club opens its door. Mr. Mehan, in his typical engaging manner, makes all the sessions enjoyable and exciting. When asked about the benefits of joining the club, Mr. Mehan explains, “students [in math club] are exposed to different kinds of math problems that they may or may not be exposed to during school. Most importantly, I just want students to have fun socializing while doing math.”

Indeed math club creates an opportunity to mingle with students who have a similar interest while improving mathematical thinking. Yashaswi Manneru ’21 agrees, “I have a great interest in math. Math club helps me to have more opportunities to express that interest.” In addition, Math Club cultivates the spirit of cooperation and teamwork. All of us, working in small groups, contribute to solving problems. As one of the members of the Middle School Math Club, Elisabeth Gadzic ‘21, states, “Math has always been a big part of my life: my parents enjoy math, so I came to love it myself. Joining math club was an exciting and cool experience. I am able to develop my skills and area of expertise.” Elisabeth also says, “collaborating with other people is my favorite part of this afterschool program because we can learn other ways of completing problems.”

Middle School Math Club offers challenging problems to test our mathematical skills and logical thinking. Megan Gupta-She ’21 adds,  “Math is a fun subject for me, and the most exciting thing about Math Club is the competitions we have and learn from.” During one of our sessions, we tested our knowledge and logical thinking as we took the official AMC-8 (American Mathematics Competitions).

Overall, Math club can be an amazing experience that can be both fun and rewarding: meeting and socializing with fellow Philomaths (math lovers) while developing our critical thinking capabilities. Here is one of Raymond Smullyan’s puzzles to test your thinking:

On a fictional island, all inhabitants are either knights, who always tell the truth, or knaves, who always lie.
John and Bill are residents of the island of knights and knaves.

Question 1
John says: We are both knaves. Who is what?
Question 2
John: If (and only if) Bill is a knave, then I am a knave. Bill: We are of different kinds. Who is who?


Solution to Question 1:

This is what John is saying in a more extended form: “John is a knave and Bill is a knave.”
If John were a knight, he would not be able to say that he was a knave since he would be lying. Therefore the statement “John is a knave” must be true.
Since knaves lie, and one statement is true, the other statement must be false. Therefore the statement “Bill is a knave” must be false which leads to the conclusion that Bill is a knight.
The solution is that John is a knave and Bill is a knight.

Solution for Question 2:

John is a knave and Bill is a knight.
In this scenario, John is saying the equivalent of “we are not of different kinds” (that is, either they are both knights, or they are both knaves).
Bill is contradicting him, saying “we are of different kinds”.
Since they are making contradictory statements, one must be a knight and one must be a knave.
Since that is exactly what Bill said, Bill must be the knight, and John is the knave.


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