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Mathematics Illuminated: Perfect Shuffles in Theory and in Action

Dr. Yat Ming Chan from the Department of Mathematics gave a public lecture on group theory on April 9 to over 120 participants, most of whom were secondary school students. TELI enhanced the event with real-time polling activity and an interactive demonstration of “perfect shuffle” using gigantic poker cards.


Group theory is an important area of study in abstract algebra. Using the examples of mattress flipping and contra dance, Dr. Chan explained to the audience the four conditions of being a group, namely, closure, associativity, identity and invertibility. While these big terms and concepts might be too abstract to first-time learners, Dr. Chan checked their level of understanding by posing this question on mentimeter, the online polling tool:

“How many perfect shuffles do you think it will take to restore a deck of 52 cards to its original order?”


Many “confessed” through anonymous submissions that they were just randomly guessing. Therefore, Dr. Chan invited 9 students to go on stage and demonstrate what would really happen when we shuffle the 10 cards perfectly (i.e., divide the cards into two equal decks, and then interleave them one by one). This activity presented an opportunity for participants to creatively take ownership of their learning.


Dr. Chan concluded his lecture by showing participants how group theory can be used to appreciate symmetry in 3D shapes (using, wallpaper designs, and other specialties in science.

TELI supports STEM education. We see ourselves facilitating best practices in STEM through e-learning, and we are keen to discuss plans about making the younger generation of learners curious explorers of the world. If you’d like to collaborate with us, please get in touch by emailing