How Many Options for a Date?
An animated four-chapter journey where you help Ben prepare for a date while learning the core concepts of combinatorics.
Combinatorics is a curious area of mathematics. For a long time, even AI struggled with the simplest problems because it requires precise attention to detail, the ability to break a problem into simple steps, and the ability to distinguish between outcomes.
The learner is invited on a journey through a 4-chapter story in which the protagonist, Ben, prepares for a date and faces many choices.
Each chapter explores a different combinatorics concept: the multiplication principle, permutations, arrangements, and combinations. Each concept opens the door to the next through restrictions on decision-making. This shows learners that all concepts are interconnected, and that choosing the best one for a given situation depends on what defines a different outcome: the number of choices and/or the order.
The animation was structured to give the thinking tools needed to deconstruct a counting problem into different steps, an essential skill in combinatorics, as referred to previously.
The formulas and application rules are given only at the end, after students have grasped the concept and representation. This reduces the perception of randomness in these formulas and connects them to something the learner understands, so that even without them, they can still solve counting problems.
Each formula is derived from the previous formulas learned. This creates a learning progression and a connection between all the terms.